
...' \ ", 



'.•!• I >r ' >» 






it'i' 



'■■ '.v ; 



PTIONHL TUBE WORKS GO,, 

Manufacturers of 

Bpecial Lap-Welded Pipe 

Fitted with 

Converse Patent Lock Joint. 




TRADE MARK. 

This special pipe is well adapted for the conveyance of water, gas 
or air, under either light or heavy pressure; is tested and guaranteed 
to stand 300 pounds per square inch, and is thoroughly protected 
against corrosion or the action of any acids or alkalies found in na- 
ture. 

It can be bent or roughly handled without cracks or injury and 
can be laid more RAPIDLY AND CHEAPLY than any other style 
of pipe; a great saving in freight being effected on account of its 
LIGHT WEIGHT. The great saving in friction in this pipe enables 
SMALLER sizes to be used and equal results obtained, and a conse- 
quent saving in first cost. 

The lengths average about 18 to 20 feet and require about one-half the 
quantity of lead per joint that cast iron does. The joint with the pipe 
has successfully stood an hydraulic pressure of over 1000 pounds per square 
inch in tests that have been made. Kalamein alloy. imparts nothing inju- 
rious to water, and Kalamein pipe may be safely used to convey drinking 
water without any fear of contamination. This pipe recommends itself, 
through its many desirable features, to the consideration of all who con- 
template using pipe for water or gas works. Information and prices 
promptly furnished. A complete line of Fittings, Valves, Hjdrants, Tools 
are manufactured by us in connection with this piipe. This pipe 



etc., etc., 
is used in 



pipe. 1 nis pipe 
over 400 cities and villages in the United States ; nearly 2000 
nules Jiavjng been laid in tlie i>ast eight years. 



W. p. BUTLER, 

GIUIL S IRRIGfiTIOMNGlNEER, 

Irrigation Wori^ 

AND 

Water & Sewage f lants 



DESIGNED AND SUPERINTENDED. 



T"o\A:)n*-Sit€ platting a speeia 



ialtif. 



Reservoirs i^aid Oat. 
pitehes & grains ©raded. 
plames J7esigned & l^aid Oat 
5^stimate8 /Aade. 



Designing and Qrawing 

plain or Qeeoratiue. 



Roate laid Out, Farm lines Ran and Corners Relocated. 



Copies of This Book For Sale, 25 Cents. 
W. P. BUTLER, ABERDEEN, SOUTH DAKOTA. 



IRRIGATION MANUAL, 

CONTAINING 

Hgeful Infopmatioi? and (Eabkg 



APPERTAINING TO 




^ 






"ii"*^ "p^ 1? [iw >ii iir I?' rti^ lilt 

■^ j^ ^^ ^ly imN^/ii/ w ^i' i^^ •11' li 






BY 




IN THE STATES OF 



BoFtt/ and South Sakota, 



TOGETHER WITH 



Many Tables, Rules, and Items of Miscellaneous Information, 



OF VALUE TO 



FaFiiiEF? and Bu^ihe^s ffien. 



BY W. P. BUTLER, 

Civil and Irrigation Engineer, Aberdeen, S D, 

1892. 



" Let tldnga that have to he done he learned by doing them.'' 



HUKONITE PRINTING HOUSE, 
HURON, S. D. 



^.1? 



Entered^ according to Act of Congress, in the year 1892, hv 

W. P. BUTLER, 

in the office of the Librarian of Congress, at Washington. 



PUBLISHERS' CERTIFICATE. 

Huron, S. D., June ist, 1892 

The publishers of this book hereby certify that, in accordance 
with the orders of the author, they have printed and hound 3500 
copies of the same. 

SHANNON & LONGSTAFF, 

Publishers. 






4-^ 



A 



.V / 



^^ 



Vn^ INDEX TO TABLES. 



TABlrE SUBJECT. PAGES 
NO. 

1 Dimensions of Standard wrought iron pipe 16 

2 Prices " " 17 

3 Comparative prices of different pipes 18 

4 JPrices and sizes of x and xx strong pipes 19 

5 •' " " " casing pipe 20 

6 Comparative weights of different pipes 21 

7 Dimensions of pipe couplings 22 

8 '' and weights of Kalamein pipe 22 

9 Relative areas of standard pipe 23 

10 Weights and sizes of cast iron pipe 23 

11 " sizes and prices of spiral riveted pipe 24 

12 American and Birmingham wire gauges 25 

13 List of Dakota artesian wells 39 

14 Precipitation during irrigating season in Dakota 44 

15 Water duty in Colorado 46 

)'■ " '• " Dakota.... 48. 

: 7 Weir measurement table 56 

' Table of Miner' s inches rechiced to cu. ft. and gallons 58 

],} " " " inch measurements 59 

20 " •' Second feet reduced to gallons 60 

21 A'olume and Weight of water on one acre 61 

22 Weight of water in pipes 62 

23 •' " " 63 

24 Pressure of •' 64 

25 Volume and Weght of water in 9oo feet of pipe 65 

26 Diameters, areas, and contents of pipes in cu. ft. and gallons 66 

27 Relative discharging capacities of pipes 67 

28 Friction loss in pipes, velocity to 7 feet 68 

29 " " '• '* " " 20 " 71 

30 Tabular numbers for computation of flow of water in pipes 72 

31 Horizontal and vertical distances reached by jets 63 

32 Table for calculating the liorse power of water 80 

33 Volume per minute = to a given flow per day, and \ 

Volume per day = to a given flow per minute ) 83 

34 Time required to flood different areas to different depths 84 

35 Volumes thrown in different times by wells of different volumes 

per minute 86 

36 Cubic feet reduced to gallons and gallons to cubic feet 87 

37 Volumes from different sized wells in 1 and 3 months 88 

38 Discharge of jets in gallons per minute 89 

;^ Size and capacity of wind mills 90 

40 Volume pumped per miunte by wind mUls 90 

41 Velocity and force of wind 90 

42 Wind in Dakota, for past 9 years 91 

43 Rain •' " " " 10 " 91 

44 Cross sections of reservoir banks 101 

45 Reservoirs, areas, diameters, and circumferences . . 102 

46 " , loss by evaporation and filtration 103 

47 " , areas, diameters, circumf's and contents of banks 104 

48 " . '• , and volumes at different depths 105 

49 '• ,cost 106 

50 ', , flow of water from 107 

51 Depths, slopes, areas, perimeters. &c. of ditches 113 

52 Grades per mile and per 100 feet 116 

53 Irrigation statistics — from census reports 137 



B 
Index to Tables — Continued. 

NrXBEK. SUBJECT. PAGES. 

54 Table of time 154 

55 " " wages— 3 tables 155 

56 Sizes of a one acre field 156 

57 Square feet in different areas 156 

58 Hills on one acre 157 

58V^ Measurement of angles by a 2 ft. rule 158 

59 Tables of nails and spikes 160 

60 " •' wrought " 160 

61 " " Manillarope 160 

62 " " weUdigging 161 

63 Capacity of cisterns for each 10 inches of depth. 161 

64 •' " " in wine barrels 161 

65 Lumber table— joist 163 

66 '• '' boards 163 

67 Decimals of a foot for each 1-32 inch 164 

68 " " an inch for each 1-64 inch , 165 

69 Square roots of 5th powers of numbers 166 

70 Lengths of circular arcs 167 

71 Table of circles, areas and circmuf 's, diameters in eights 169-171 

72 •' " " " " '• " " tenths.... 172-171 

73 " " " •' •' " " •' twelfths.. 178-184 

74 Table of sq. and cu. roots 1 to 28, advancing by tenths 185 

75 " " " " '' " ItolOOO 186-193 

76 •' •' •' •' " " lOOOtolO.OOO 194-197 

77 '• •' Logarithms 198-200 

78 •• " Tangents and cotangents 148-149 



INDEX TO FIGURES. 

FIG. 

1 Section of lap-weld and butt-Aveld pipe 14 

2 " " pipe couplings 20 

3 Specials and pipe fittings 21 

4 Section of a "telescope" well 27 

5 Perforated pipe in well 28 

6 Spill-box 52 

7 lUxTstrating contraction on weirs 53 

8 Weir, and method of water measurement 54 

9 Miner's inch measiirement 58 

10 •' " '• 59 

11 Method of measuring the height of a stream 93 

12 Rainfall and temperature map of Dakota 94 

13 View of the Yankton well 95 

14 Slope diagram for reservoir banks 98 

15 Section of reservoir and bank 105 

16 Form of gate in reservoir bank 108 

17 Section of ditches Ill 

18 '• " ditch 112 

19 Pulsometer pump view 127 

20 " •' " 128 

21 Simple form of level..., 130 

22 Leveling rods 131 

23 Scales — decimal and duodecimal •. 135 

24 Measurements between inaccessible points 147 



c 

GENERAL INDEX. 



Aberdeen well ;3<s ;i9 

" sewer plant 78 

Acre, size of circular — li)7 

•' foot 60 

'• " defined 51 61 

" Hills on an - 157 

*' Size of one — 156 

Acreage, to compute 156 157 

Angle. Complement and supple- 
ment of an— 152 

Angles. Measurement of— by a 

2 ft. rule 158 

Apparent level 135 

Apples in bin 162 

Area of farms 45 139 144 

•' " fields 156 157 

'• Relative— of pipes 23 

Arizona. Irrigation statistics of .137 

Artesian wells elewhere 37 

" in Dakota 38 41 

B 

Barrel. Contents of a— 162 

" Weight of a — of water 63 

Board measure tables 163 

Brick 162 

Butt welded pipe 14 

C 

Casing pipe. Prices and Sizes of .20 
Cast iron pipe. Sizes and weights 

of— 23 

Center of pressure 42 

Characters . Explanation of— . . . 203 

Chimnej's 162 

Circles. Elements of— 152 153 

" Explanation of tables of .168 
" Tables of— diam's in Sths, 

169 to 171 

" Tables of— diam's in lOths 

172 to 177 

Tables of— diam's in 12ths 

178 to 184 

Circular arcs. Table of— 167 

Cisterns. Capacity of— for each 

10 inches 161 

" . Capacity of — in wine 

barrels 161 

Conclusion 204 

Contents of pipes 66 

Corn and hogs 154 

'' in bin 162 

Cost of ditching 117 

" " wells .34 36 

Couplings. Kinds of— 18 

'• Tables of 22 

Cubic ft. on one acre 61 

" " " different areas 84 

•' " in pipes 66 

'• " ''reservoir 105 

'' " per sec. reduced to gals.. 60 
'• ''reduced to Miners inches. 59 

58 

■' " " ■' gallons 87 

" " thrown in 1 and 3 months.SS 

" foot is equal to 151 

Cubes, squares and roots 185 197 



Dakota wells :}S 

•• Table of- 39 

Datum plane 129 

Day. Astronomical— 154 

" Siderial— 154 

•' Mean Solar— 154 

Decimals of a foot for oacli 1-32 

inch 164 

"an inch for each 1-64.165 
Diameter. To find— to discharge 

given volume 72 

Digging wells 160 

Discharge from pipes 69 70 

" To find volume of— of 

pipes 72 

Discharging power of i)ipos. Rel- 
ative— 67 

Ditches llO to 120 

" Area of section 112 113 

" ( 'tJiitents of excavations of.ll9 
Ditching machines for— . . 

Ill 117 118 

'■ Embankments and foot- 
ing of 118 

" Excavation and cost of. 117 

Flow of water in— 113 

" Form and size of— 110 

" Gates in— 119 

Grades of— 1 15 116 

" Location of- 120 

■' Laying out — 117 

Length of wet perimeter 

of—.. 112 

" Maximum velocity of 

water in — 114 

" Mean velocity of water 

in— 114 

" Small lateral— Ill 

" Slopes of— 113 

'* Table of areas of — 113 

" " grades of— 116 

" Widths of— Ill 

Division and measurement of 

water 49 

Divisors for water .51 

Drilling. Suggestions as to — .33 

Drive pipe 15 

Duty of water 43 to 48 

" '■ *' in Colorado 46 

" " " Dakota 47 

•' •• •■ " table 48 



Embankments and ft)(>tings. . . .118 

Entry head 69 

Excavation. Cost of — 117 

Excavations. Contents of — 119 

Extra and xx strong pipes 15 

Evaporation and filtration 103 



Farmer. The — 8 

Farms. Size of— 45 137 142 

Feet. Cubic— see cubic feet ....... 

' ' Second— reduced to gallons . 60 



D 



General Index— Continued. 



Fields. Area of— 156 157 

" Laying out — 120 

Filtration from reservoirs ICK? 

Flow of wells per day and per 

minute .8:3 

Flumes. ... .., 120 to 122 

Formula for weir measurements. .57 
Foot. Acre— defined 51 

" Cubic— see cubic feet .. 

" Decimals of a— 164 

' ' Second— defined 60 51 

Footings for banks US 

Francis' formula for weirs 57 

Friction head defined 67 70 

' ' loss in pipes 68 to 72 

Frosts in Dakota 92 



Gage groupe of wells in Cal. . ;38 1:36 

Gallons^ to 1.51 

" in pipes 66 

" ''reservoirs 105 

" on different areas 84 

" " one acre 61 

' ' per minute defined 51 

'■ '• day = to given gallons 

per minute 83 

" per minute — to given gal- 
lons per day 8:3 

'■ reduced to cubic feet 87 

"second" ,...60 
" tlirown in different per- 
iods of time by wells of 
different volumes per min- 
ute 86 

' • tliTown in 1 and :3 months . .88 

" by jets 89 

Gates 41 107 119 

Gauges. Water- 65 

'' Wire — 25 

Grades of ditches 115 116 

" Tableof— 116 

Grain in bin 162 

H 

Hay 162 

Head defined 69 

" Entry- 69 

■' Friction— 69 

" Velocity— 69 

'• To find— 72 

Height of a stream. To meas- 
ure— 9:3 

Hills on an acre 1.57 

Hitchcock mill .81 

Hogs and corn 154 

Horse power defind 82 

Horse power of water. To find 

the— 80 

Hydrants 29 

Hydraulic mean depth 112 

" radius 112 

" ram 124 

Idaho. Irrigation statistics of— 1:37 
Illustrations, see index to Figures 
page B 



lucli. Decimals of an — for each 

1-64 165 

" Miner's- 5158 59 

•'in California 59 60 

'• •' Colorado 59 60 

" " measurements 59 

'.' " reduced togaUons and 

cubic feet 58 

" Statute — defined 51 

Irrigation. Early history of — .6 76 

" in Dakota 7 

" statistics from census 
reports .1:^7 

J 

Jets. Discharge in gallons from. 89 

" Distances reached by — 73 

*' To find altitude reached by— 73 
■' " " discharge of — 73 

K 

Kalamein pipe %i 

L 

Lap-welded pipe 14 

Land. Value of— 1:37 1.39 141 

Lath 162 

Level. The— 129 

" measurements 135 

" rod 131 

" Simple form of — 130 

'* True and apparent — 135 

Leveling explained 132 

" for a reservoir 1:3:3 134 

" Form of — note book 1:32 

Location of ditches 120 

•'well 31 

Logof weU 31 :32 

Logarithms. Explanation as to 

tableof— -201 

Tableof— 199 200 

Useof— 202 

" " tables of—. ..201 

Longitude, length of degree 164 

Lumber 162 

" tables 163 

M 

Machines. Cable— 12 

Ditching— ....111 117 118 

Hydraulic— 13 

Jetting—.... 13 

Kinds of— 11 

Pole- 11 

Mean depth 112 

" radius 112 

Measure. To — the height of a 

stream 93 

Measurement of angles by a rule.158 
" and division ofwater 49 
*' of water by a weir. .53 

" Units of — of water ... 51 

Measures and weights 150 to 153 

MelviUe law, 8 31 

Mensuration 150 to 153 

Millsites 79 

Mills at Hitchcock 77 78 81 



E 



General Index — Continued. 



Mills at Spriuglield 81 

" '• WooTisocket 78 81 

" Yankton 81 

"' run by wells 77 78 81 

Miner's inch 31 38 

" in Cal. and Col 59 60 

" " reduced to gals and 

cu f t oS 

Miner^s inch measurements 39 

Miscellaneous information 162 

Module defined 51 

Montana. Irrig'n statistics of — 137 

Mortar 162 

Multipliers. Useful— 153 

N 

Nails. Tables of— and spikes. . .160 
Nettleton. Letter from Col. E. S..73 
Nevada. Irrigation statistics of. 137 

New era grader and ditcher 117 

New Mexico. Irrigation statistics 
of— 137 



Outlets and gates 41 107 

P 

Perforated pipe 28 

Perimeter. Wet— 112 113 

Photographs of wells 1-13 146 

•' Description for — . . .144 
" List of — and pho- 
tographers 146 

Photographs. Where to buy — . . 146 

Pipe 14 to 28 

" Butt welded— 14 

" Casing — , prices and sizes. . .20 

' ' Cast-iron— 23 

" Contents of— 66 

" Drive- 13 

•' Friction loss in — 68 to 72 

" Kalamein— 22 

'• Lap-welded — 14 13 

*' lines. Advantage of — 123 

" '' for distribution.. . 122 123 

• • Per f ora ted— 28 

*' Prices. Comparative — of — .18 

" Prices of standard — 17 

" Relative areas of — 23 

'■ " dischargmg powers of — 67 

" Spiral riveted— 24 

" " welded— 27 

'I Standard— 16 

"' Vertical opening to — :% 

" weight of— Comparative— ..21 

'' Weight of water in — 62 

" X and XX— 13 

" '■ Prices and sizes of— 19 

Polygons 133 

Power. Horse— 82 

" of weUs 77 to 82,204 

' ' To calcula te horse— 80 

Precipitation. Distribution of— 44 

" - in Colorado 44 

•'Dakota... 91,92 

" •' *' in April 
and May 44 



Precipitation map of Dakota 94 

Pressure and vohime. Relation 

between 9 

in 900 feet of pipe ..65 

of water, table 64 

Static— 9 

To find — of water 64 

Prismoidal formula 157 

Pumps 125 to 128 

" Cost and duty of — 125 126 

" Pulsometer— 126 to 128 



Rain making 26 

'* . in Colorado 44 

" " Dakota 44 91 92 

Ram. Hydraulic— 124 

Reaming 14 

Relative areas of pipes 23 

" discharging capacity of 

pipes 67 

Relative weight of pipes 21 

Reservoirs 96 to 108 

" Areas, Diams, Circumfs 

of— 102 

" Areas, Diam's, Circumfs 
and cubic capacity of 

banksof— 104 

'' areas and capacities at 

different depths 105 

'' Banks of — 

99 100 101 104 117 119 

Diagrams of — 100 

Sections of— ..101 

Washing of— ..100 

•• Capacity of — at different 

depths 105 

Circumferences of — ... 

102 to 105 

Costof— 106 117 

" grading of banksof 117 
Diameters of— . 102 to 103 
Evaporation from — .103 
Filtration " ....103 

Flow " ....107 

Formof- 97 

Footings for bank of— 119 
Laying out— . . .98 133 \M 

Location of— 97 

■ Oiitlets and gates from 

41 107 108 

Sections of banks of — 101 

Size of—.. .97 102 104 105 

'• '• •• To calculate— . 103 

Slopes of banks of— . . 100 

■• Sub — and storage ditches. 108 

• Washing of banks of—. ..100 

Rod. Leveling — 131 

Rope. Manilla— 160 

Roots. Explanation as to tables 

of- 198 

'• Sq & cube— 1 to 28 by lOths 185 

" •' " 1 to 1000..186tol93 

•' •• '• " 1000 to 10000.194 to 197 

" To figure— by h)garithnis.2<X) 202 



F 



General Index— Continued. 



Scales, decimal and duodecimal. 135 

Second foot ... .51. BO 

" reduced to gallons.. .bO 

Sewer plant at Aberdeen T^' 

Shingles .v ^*?^ 

Size of farms IS"? , l-i2 

" •• pipe, see Pipe -. 

•' •' reservoirs, see Reservoirs^. 

Source and supply of water T4 

Specials ^9-^0 

Illustrations of— 81 

Setting of- 99,30 

Spikes and nails • • IW 

SpiUbox 52 

Spiral riveted pipe : . . 24 

" welded "' 2/ 

Springfield mill ••. -SI 

Square and cube roots — 185 to 197 

" roots of 5th powers 61 166 

Squares 150 to 132 

•' and cubes lt<5 to 193 

Static pressiu'e 9, 65 

Statistics of irrig"n in 7 states. . 137 

Statute inch 51 

Stonewall 1^2 

Storage ditches 108 

Stream. To measure height of a— 93 

Subject. The— 6 

Sub-rervoirs 108 

Sub-sxirf ace waters 1 25 

Suggestions as to drilling — 33 

Supply of water 74 

T 
Tables— See index to tables page A 
Tangents and cotangents.. 147 to 149 

Telescope well 27 

Temperature in Dakota f2 94 

Theoretical velocity of water 70 

Threads of pipe 18 

Time. Table of— ....154 

required for different sized 
wells to throw given volumes 

of water 84 

" Volumes thrown in differ- 
ent periods of — bj^ wells of given 

volumes per minute 86 

Ton. Weight of one— of water . . . . 63 
" " '• " " ice — 63 

Tools.... 14 

Triangles 1"2 

True and apparent level l35 

U 

Units of water measurement 51 

Useful multipliers 153 

Utah. Irrigation statistics of — 137 

V 

Value of land 139 to 141 

"water 136 to 139 

Valves 29 

Vegetation and water 76 

Velocity head 69 

Maximum sxu'face — in 
streams 114 



Velocity Mean— of streams 114 

" of sound in air 90 

■' '■ •' ■• water 90 

Theoretical— 70 

of wind 90 

.. in Dakota 91 

" weUs. To get the— ..S2 

Volume of weDs 50 

' • • ' • • per day & per min 83 
•• in 1 (t 3months...88 
•' "'in different peri- 
ods of time 86 

' ' of wells in different per- 
iods of time 60 

" on one acre 61 

" •' different areas 84 

" Relation between — and. 

pressure 9 10 

" To compute — discharged^ 
by pipes 72 

W 

Wages, Table of— 155 

Water ^'^ to 76 

" and vegetation <o 

" Annual cost of— 138 

•' Center of pressure of— 42 

•• Density of— 63 

" Distribution of— 109 to 128 

by ditches. 110 to 120 
■' fivimes..]20tol22 
• pipes... 122 to 123 

" •• ■■ ram - . 124 

•' •• •• ijumps & wind 

miUs 124 tolas 

" Division and measurement 

of- 19 

" Duty of- 43to48 

•• ' '• — in Colorado 4o 

'■ " — •• Dakota.... 47 48 
•' •' " — Referesnces to — 45 

" Evaporation of— 103 

" Flow of— in ditches. .113 to 114 
" Friction of— in pipes . . .68 to 72 

" Head of- 69 

•' Horse power of — "0 

• ' in reservoirs .- • 105 

" Maximum surface velocity 

of- 114 

" Mean velocity of— H* 

" Measurement and' division 

of- .- 49 

" Measurement of— by a weir .03 

" " units of — 51 

" on one acre, vol and weight. 6r 

" •• different areas 84 

*' Phreatic— ^25 

" Pressure of— 42 t4 

Center of— 42 

" '•' to find— 64 

'• Properties of — 42 

•' Seepage of— 4b 

' ' Source and siipply of— '4 

" Sub-surface- v'^'^ 

" Units of measurement of— . 51 

'• Value of- 136 to 139 

•• Velocity of— 114 



a 



General Index— Concluded. 



Water Voluiiic of — in pipes. . . . 6() 

■ — on 1 acre (>1 

■ — on dift'erent 

areas — ••84 

" Weightof- ...63 

" " " — in pipes 62 

" '• " — on an acre 61 

, •• ." bbl., gal., qt., pt, 

&c of- 63 

Weather in Dakota— table 5!2 

Weight of cuft of substances — 159 
" " different pipes. 16 to 24 

" " water (11 to 65 

Weights and measures — l-oO to ITiS 

Weir 51 

" Application of — table.... 55 
" Conditions of operation of a— 

52 53 

" Formula for — measurements 57 

" Illustra tion of a — 53 54 

" table 56 

" To construct a — 53 

Weisbach's formula 70 

Well^ Aberdeen- 38 39 

" digging 161 

WeUs. 'v."ost of— :34 36 

" Dakota- 38 41 

" Table of— :39 

" Economy of large and small 10 

" elsewhere 37 38 

" height of stream of — To 
measure 93 



Wells Location of— 31 

" Logof— 31 .32 

" Number in Dakota 9 

" Photographs of— • . . 145 to 148 
" " Where to buy— 148 

" Power of 65 & 67 to C2 

" Source & supply of water of .74 

" Telescope 27 

" used for mill power 77 to 81 

" Velecity of flow of 65 

" •' 'To get-. .82 
" Volume of — not dependent 

upon size 9 

" Volume of — per day and per 

minute 83 

" Volume of— in 1 & 3 mos ..... 88 

Wet perimeter 112 113 

Wind in Dakota 91 

" mills 27 90 126 

" Velocity and force of — 90 

Wire gauges 25 

Woonsocket mill HI 

Wyoming. Irrig'n statistics of — 137 



X Y Z 

X and XX pipe 15 

" " prices and sizes of. 19 

Yankton mill 81 

Yard. A cubic— is equal to— — 151 



INDEX TO ADVERTISEMENTS. 



Abendroth & Root Mfg Co. . 238 239 

Addyston Pipe & Steel Co 216 

American Well Works 252 

Austin, F. C. Manfg Co 218 219 

Belknap Motor Co 237 

Blair Camera Co 222 

Brass & Iron Works Co 225 

Buff & Berger 215 

Butler, W. P 2 

Chapman Valve Co 210 

Chicago Water Motor Co 211 

Clow, J. B. & Son 206 

Crane, Gr. W. <fe Co 213 

Consolidated Land & Irrigation 

Co 251 

Dakota Irrigation Co 245 

Dennis Long & Co 217 

Engineering Magazine 231 

" News ...208 

First National Bank 250 

Gurley, W. & L. E 220 221 

Harper &. Brothers 240 

Irrigation Age 209 

Leff el, James, Co 229 

Ludlow Valve Manfg Co 224 

National Tube Works Co., Front 



Cover and 1 

Nye Steam Vacuum Pvimp Co. . . 247 

Oil Well Supply Co 227 

Pech Manfg, Co 223 

Pelton Water Wheel Co 256 

Pulsometer Pump Co. ...127 128 244 
Railway — Chicago k, North 

Western 230 231 

Railway — Chicago, Milwaukee 

ct St. Paul 232 2.33 

Railway— Great Northern 235 

" Northern Pacific 236 

Reading Iron Co. (Back Cover) 

Rife's Hydraulic Engine Co. . 214 

Robinson & Cary Co -42 

Swan Brothers 243 

" ct Stacey (W. E. Swan Co.) .228 

Trau twine, J . C 215 

Valley Land A: Irrigation Co 250 

Western Wheeled Scraper Co.. .246 

Williams Brothers 207 

WeU Machine k Tool Co 212 

Young & Son '40 241 

See Index to articles advertised on 
next page. 



H 



INDEX TO ARTICLES ADVERTISED. 



Banks. ! 

First National, Huron, S. D. . . 250 j 
Boilers. 

Oil Well Supply Co '^27 

Robinson & Cary C o ^"^^ 

Books. I 

This book, W. P. Butler. 2 41 | 

Engineering, J. C Trautwme. . . ^lo 

Irrigation, Irrigation Age ^UJ 

Harper's Periodicals ^*y i 

Cameras. \ 

Blair Camera Co 222 

Coffee Mills and Dynamos. 

Belknap Motor Co ^3/ 

Civil Engineer. 

W.P.Butler. - 

Drillers. 

Swan Brothers 243 

Swan & Stacy 228 

Electrical Supplies. 

Belknap Motor Co 2:^7 

Engineer inci Publications. 

Engineering Magazine 234 

News 208 

J. C. Trautwine 21o 

Hydraulic Ram. 

Rite's Hydraulic Engine Co 214 

Hydrants. 

See Yalves 

Irriqation Cotnpa n ies. 
Consoldated Land & Irrigation 

Co 2.^1 

Dakota Irrigation Co s4o 

YaUey Land & Irrigati<in Co . . - .2.50 

Levels. 

Buff ct Berge/ 215 

W. and L. E. Gurley 220 221 

Young & Son 240 241 

Machines— Ditching and Grading. 

F. C. Austin Maufg Co 218 219 

^Yeste^n Wheeled Scraper Co . . . 246 

Machines— Well Drilling. 

Vmericau Well W' orks 252 

Austin, F. C, Mfg. Co 218 219 

Brass & Iron Works Co 22o 

Oil Well Supply Co 227 

Pech Manf g. Co 223 

W^eU Machine & Tool Co 212 

Williams Brothers 20 1 

Machines— Road. 

F. C. Austin Mfg. Co 218 219 

Western Wheeled Scraper Co. . .24« 



Motors— Electric and Water. 

Belknap Motor Co ' "^1 

Chicago Water Motor Co ^Jl 

.las. LefEel Co 229 

Pelton Water Wheel Co ■«'«> 

Pipe— Cast -Iron. 

Addyston Pipe & Steel Co 216 

Dennis Long & Co ^^^ 

Robinson & Gary Co ^^ 

Pipe—Wroufjht Iron. 

American WeU Works 252 

.J. B. Clow & Son ^ 

G. W. Crane <fc Co r^ T 

National Tube Works Co., Front 

Cover and iij 

Oil Well Supply Co. 227 

Reading Iron Co., Back Cover. .... 

Robinson & Gary Co «*'^ 

Pipe— Riveted. 

Abendroth k Root 238 239 

Pumps. 

American Well Works ;^- ■ • '^^^ 

Nye Steam Yacuum Pump Co. . .247 

Oil Well Supply Co .... 22. 

Fulsome ter Pump Co. .127 128 244 

Robinson A: Gary ^^ 

Railvays. 
Chicago k Nortliwostern . . . .'^0 231 
" Milwaukee & St. P. 332 233 

Great Northern 23o 

Northern Pacific --* 

Scrapers. 

F. C, Austin Mfg. Co ■ 219 

Western Wheeled Scraper Co....^^ 

Specials— for Pipe. 

Addyston Pipe & Steel Go 216 

Dennis Long <t Co ^^ 

Robinson <fc Gary Go «*^ 

Steam Goods. 

G. W. Crane & Co 213 

Valves. 

American Well Works 252 

Brass & Iron Works Co |»o 

Chapman Yalve Co . ^W 

Ludlow Yalve Mfg. Co ....... -224 

National Tube Works Co., Front . 

Cover and • • ^ 

1 Robinson & Gary Co ^'*'' 

Water Wheels. 

See Motors 

TT'e/7 Machinery. 

\ See Machines— well drilling 

Wind MilU. 
Pech Manfg. Co 223 



PREFACE. 

The idea in presenting this little book to the public is to 
supply, in part, a demand for such tabulated and general in- 
formation as is needed by many, at the present time, who 
are becoming interested in the matter of irrigation. Few 
have access to books of tables and rules and fewer still are 
able, without them, to figure out the problems involved, and 
bence, many abandon the subject because unable to culti- 
vate an interest sufficiently satisfactory to themselves to 
warrant the taking of some definite step in the direction of 
a practical trial of that which, if properly managed, must 
open up the road to fortune to all who choose to enter. 
The idea is not to present an exhaustive treatise on irriga- 
tion, or to treat at length any of the matters presented, but 
simply to suggest them and, by giving many rules and tables, 
to supply trie information needed, so that each may, for 
himself, make such estimates as the circumstances of his 
own case may require; and further, to put the investigator 
in the way of obtaining such desired information as cir- 
cumstances would not permit of being given here. 

In the selection of many rules and tables the following 
standard works have been freely consulted and properly 
credited : 

Haswell's Eugiiieer's Pocket Book, (Harper & Bros., New York.j 

Trautwine's Engineer's Pocket Book, (John Wilej- <k Sons, New York.) 

Engineer's Pocket Book, 1876, (Lockwood <fe Co., London.) 

Uuseful Information, (Jones & Laughlin, Pittsburgh.) 

The Measurement and Division of Water, (L. G. Carpenter, Ft. Collins, 

Colorado.) 
Pocket Companion, (Carnegie Phipps & Co., Pittsburgh.) 
The trade cataloges of the Chapman Valve Mfg. Co., National Tube 

Works, James Left'el <k Co., Addyston Pipe Co., Pelton Water Wheel Co., 

Reading Iron Co., and others. 
State and government reports, and all other available and reliable 

sources, such a? the' Engineering News, Irrigation Age, and Scientific 

American. 

Besides the matter thus compiled, many entirely new 
tables have been computed to answer the special require- 
ments of those to whom this matter is addressed. 

If the matter presented is instrumental in creating any 
new, or in fostering any present interest in irrigation, or in 
aiding any in need of such information as is presented, then 
will the object of the compiler have been accomplished. 

In the hope that hereby a demand has been partially sat- 
isfied this little book is inscribed to the advocates of irriga- 
tion in the Dakotas, by 

W. P. BUTLER, 

Compiler. 



THE SUBJECT. 

Much valuable time is wasted in the preparation and 
printing of articles on irrigation the burden of which seems 
to be to remove a doubt as to whether irrigation will pay, if 
practiced in the Dakotas. 

The chief object accomplished by such articles is to keep 
alive the very doubt they aim to overcome, and at a time 
when, and in a place where, a doubt will do the most harm. 
The only good accomplished is that the subject is kept open 
and before the public. 

THERE IS NO DOUBT 

as to irrigation paying in Dakota, and this may be abund- 
antly shown by a study of the history of irrigation in this 
and other lands. 

Irrigation is as old as the race and it has been both the 
heritage and the legacy of every tribe and nation. The 
dawn of history dimly reveals the practice by those ancient 
peoples, and history, both sacred and profane, has recorded 
its onward march, as it has the march of armies. In Pales- 
tine, in Egypt, in Assyria and in India it was, as it still is, 
the life of the people. As irrigation developed, empires 
arose, and with its fall they fell ; and where was once the 
verdant homes of countless millions there is, to-day, a des- 
ert waste. 

The legions of Rome may be said to have been supported 
by irrigation; for the Roman Empire was but a union of ir- 
rigated nations. The subject in that day having the sanc- 
tion and fostering care of every monarch. As the world has 
developed so has irrigation — until to-day, a large percentage 
of the products of the world are raised by that means; and 
now, as in all past ages, those who till the soil under a sys- 
tem of irrigation are the most prosperous of their class, and 
their lands the most valuable of all devoted to purposes of 
agriculture. 

Irrigation has developed during these ages, as has every- 
thing else; now progressing, and again declining, with the 
progress or decline of the arts and peoples of each age and 
nation. The system of Spain was not that of Italy, nor is 
the system of to-day the same as that of a century ago. 

The literature of irrigation is most interesting, and every 
irrigator in the Dakotas should "read up" to the fullest ex- 
tent. 

The system of irrigation practiced in every country has 
been a development, not alone in its engineering sense but 
in its legal sense also ; for the questions of water rights and 
appropriations have always been most intricate and have 
demanded most studied treatment. 

Irrigation in the United States was first practiced in the 
Salt Lake valley and in lower California, although very ex- 
tensive systems of irrigation works, built by the aborigines 



were in ruins when the earliest settler went into the country. 

The ancient inhabitants of Mexico and of Peru had vast 
systems of canals, aqueducts and tunnels for the purpose of 
water supply and irrigation, so that the industry of the 
white man is but a revival, on this western continent, of the 
older irrigation system of the ancients. 

From the. crude beginnings of the pioneers who lacked 
both capital and labor, and were forced to begin anew, with- 
out previous knowledge of the subject, and under new con- 
ditions, there has developed in our western states a system 
of irrigation so vast that its worth is measured by the tens 
of millions, and so perfect as to bear most favorable com- 
parison with the older and highly developed systems of 
Spain, Italy and India. Each state has done all in its power 
to foster the industry, to encourage investment in plants 
and securities, and, by systems of law best suited to their 
special conditions and requirements, to surround the indus- 
try with all needed protection. 

IN DAKOTA 

the day was, when to have spoken of irrigation as necessary 
to our wellfare, would have been to have uttered heresy. 
That day has passed. The bitter experience of a series of 
dry years — when the hot wind was all we reaped — has taught 
the lesson that, to live in prosperity and pleanty in Dakota, 
we must irrigate. It is no crime; it is no disgrace; for the 
most fruitful lands on the earth are such as are irrigated 
and such as would be a barren waste were it not for irriga- 
tion. Such lands are in the deserts of Arabia, Africa and 
our own western states. No better soil or climate exists on 
this continent than that of Dakota and, with water at our 
bidding, none on earth will be more f ruitf ull. 

No country in the world, so far as known, possesses what 
Dakota does— a soil of unmatched fertility, a climate suited 
alike to the best needs of plant and animal life, a topography, 
or surface, best suited to a system of general irrigation, and 
at the minimum of cost, and a supply %f water as general 
in its distribution as it is inexhaustable in its volume and 
powerful in its flow . 

What a combination is this ? Soil— climate— topography 
— water and power. Each perfect; each in accord with the 
other; and all to be had and controlled by him who wills it. 

A Dakota farmer need not wait for a rich company to 
build a dam to impound the clouds and then beg life on 
such terms as the company may care to fix. 

He has but to prick the »oil and a fountain of wealth 
pours forth to do his bidding. A servant as powerful as the 
elements, yet as subject to control as the child; more bur- 
dened with wealth than the summer shower and less bur- 
dened with disaster than the summer torrent. A servant 
perfectly trained to the performance not alone of one duty 
but of many, and a servant the like of wliich nature has not 
vouchsafed to the service of the men of any other land. 



8 

THE FARMER. 

Has he had abundant crops? No! 

Does he need, and must he have, a well? Yes! 

HOAV WILL HE GET IT ? 

No solution is offered as to the meajis, but it is giving 
good advice to say — Adopt any means. Some will be more 
advantageous than others yet to most farmers it will not be 
a matter of choice. 

ANYTHING TO GET A WELL! 

The " Melville " law, providing for township wells, has not 
been a success for, although 115 wells were located by the 
State Engineer during 1891, and bonds voted for them, no 
market (except in two cases) has yet been found for these 
bonds because of the manifest injustice of the law, which 
provides for the assessment of property not in the least ben- 
efited, or needing any benefit, in order that other private 
properties may be developed. Investors look askance at se- 
curties having so strong a taint of unconstitutionality and, 
as a result, there are few such wells being drilled; the ac- 
tivity being confined almost wholly to purely private enter- 
prises. 

A more equitable law must be passed to give relief. If 
the present law can be made to work, well and good, take 
that means. If a mortgage company, or an individual, 
stands ready, under any one of an infinite number of plans, 
to put down a well for you, take it at once. Raise the mon- 
ey in any way— only raise it! 

If you can't own a whole well, own part of one. If you 
can own it all, do so by all means, for joint ownership means 
joint responsibility and its attendent evils. 

Part of a well is better than no well, and 40 acres "under 
water " is better than 640 acres under a hot wind. Loose no 
time in stopping to figure — as many are continually doing — 
whether irrigation will pay or not, for it never did anything 
else hut pay, here or elseichere. If you want a life job take 
that of trying to prove that irrigation ever failed to pay and 
pay well. Let the first task be to get the money, figure on 
that and then when it is obtained there will be time to figure 
on its use. 

The details of an irrigation plant in Dakota are very sim- 
ple as compared with those in most other sections, where the 
sourse of water supply is at a great distance and where 
heavy dams, long and expensive flumes, tunnels and bridges 
must be built either to store or to convey it. These great 
engineering works entail a vast expense and preclude any 
individual ownership or controll. Here, however, the whole 
system of supply and distribution may be created upon, and 
limited to, ones own garden patch and at but nominal cost. 

Where other systems prevail there enters in the very com- 
plex questions of water rights, which, to a great extent, can- 
not find a place here where the system is so different and 



esseiitiaUy individual. If a farmer owns a well he can use 
it when and as he chooses, and to any extent, so long as he 
does not trespass upon his neighbor; and he may sell the 
water on such terms as he may be able to make. Nor can 
he prevent his neighbor seeking a supply from the same 
source, for whence the supply comes and what its volume 
inay be" can never be other than conjecture. 

That questions c»f water rights as between individuals, 
and as between the State and individuals, will arise there 
can be no question, but what questions will arise and what 
their solutions will be, may be safely left to the future. 

After the question of money supply, the first consideration 
is as to the well. 

THE WELL. 

About 200 wells have already been put down in the two 
Dakotas, varying in size from 2 to 8 inches. The popular 
and common sizes being i% and 6 inch wells. On the whole, 
very little is yet known of our wells because of lack of sys- 
tematic study and experiments. Then, too, very many er- 
roneous ideas prevail as to the wells and, uufortunately, any 
amount of wilful exageraation which will, in the end, result 
in more harm than good. 

A few facts will be stated and explained. 

The volume of a well does not depend upon its size, that 
is, an 8 inch w'ell will not, necessarily, discharge more water 
than a 6 inch well. The volume discharged by a well of any 
size will depend entirely on the depth of the well and the 
character of the rock in which the water is found. If the 
rock is hard and fine in texture the flow of water through it 
will be less than if the rock is soft and coarse and filled with 
pores and open channels. Again — the volume need not be 
great because the pressure is high, as many suppose. This 
is shown by a comparason of the southern with the north- 
ern wells. The southern wells having in some cases a very 
large flow and a low pressuie while the northern wells have 
a lesser volume and a much higher pressure. The former 
are not so deep, either, as the latter. 

When the well is closed the pressure is said to be a 
STATIC or standing pressure. This is absorbed in throw- 
ing out the water when the well is opened. If the pipe is 6 
inches all the way down, more w^ater will get into the bottom 
in a minute than if the opening at the bottom is but 4 
inches, and that at the top 6 inches, yet th^ pressure of the 
water will be the same wiien closed in. So, too, the rock 
may be so hard as to prevent a large supply reaching the 
pipe per minute, so the volume will be small although the 
pressure may be high. 

In this case the supply fails to meet the duty of the pres- 
sure. Other wells have a very large volume and compara- 
tively low pressure. In this case the rock is soft and open 
permitting of a large and free flow all, or only a part of 



10 

which, is thrown out. The condition is here reversed, i. e., 
the duty of the pressure lails to meet the volume of the sup- 
ply. In sinkiniif a well it is w^liolly a matter of conjecture as 
to what the volume and pressure will be. The chances are 
in favor of getting a larger volume from a larger well, but 
the pressure will not (as above explained) increase in the 
same proportion as the volume; nor will the velocity of 
discharge keep up, under a given pressure, if the well is 
larger and the volume only proportionately greater. 

The matter of relatiue economy, as between wells of dilfer- 
ent sizes, has yet to be determined, and it can only be deter- 
mined by the sinking of many wells and their careful study. 

In other countries a man having 160 acres figures in ad- 
vance on just what water he needs In Dakota a man fig- 
ures on as big a well as he can pay for and is ' hankful f©r 
whatever water the well brings hiri— the more the better. 
In figuring on what kind of a well to put do jvn do not fig- 
ure too fine, that is, do not get a small well because its esti- 
mated volume (judging from others of its size in the neigh- 
borhood) will answer your purpose, because of two import- 
ant reasons . 

FIRST, a small well will clog or stop up more easily than a 
larger one and will be more costly and more diflicult 
to clean out. 

SECOND, incase of accident dming the drilling or after 
completion, a small well, may be spoiled if recased, 
while a larger well could be recased and still leave a 
serviceable well. The smaller one might have to be 
abandoned under circumstances which would per- 
mit of the larger well being rendered serviceable. 

The larger well has thus substantial advantages in its 
favor aside from the mere matter of volume, and a few dol- 
lars extra, in the matter of cost, ought not to stand in its 
way. The increased service of the increased volume from 
the larger well would, in many cases, pay not only the in- 
creased cost but for the whole well. 

Stated generally, it would appear to be poor economy to 
put down a well of less than 5 or 6 inches diameter. What 
the economical limit above this size will be remains to be 
demonstrated. 

Having decided upon a well, of say 6 inch bore, then comes 
the details of getting it. Some will contract with a well- 
driller near at hand; others will advertise for bids, and, of 
course, accept the lowest, whether it be best the or not; 
others will seek the county rig, while still others will, either 
alone or by clubbing together, buy a rig and drill the well 
themselves. Some will f « vor one y rocess and some another; 
while some will favor one make of rig which another person 
may condemn. 

By reason, therefore, of this diversity of circumstances, 
opinion, and preferences, and the fact that, up to date, very 



11 

little systematic work has been done and no one process or 
rig has demonstrated its superiority over all others, no defi- 
nite instructions can be given as to the best course to pur- 
sue or the best method to adopt. If a CONTRACT is en- 
tered into for the drilling it is usually as a result of bidding. 
In this case the chief consideration to the farmer is as to 
size, materia], cost and time, and not as to the method or 
system used by the c ntractor. He may use poles, cables, or 
the hydraulic process, as he prefers so long as he gets a well 
in proper manner and time. 

The details of the contract are very important and it 
should be drawn up by some one who understands the value 
and importance of these details, so that there is contained 
all that should be, and in proper form, so that the rights of 
both parties will be protected. 

If all goes well the contract is a mere ornament, but if 
trouble arises the contract comes out and then every word 
has a value. The contract is to the controversy what the 
safe is to the fire, 

From the information contained herein it is expected that 
any man, familiar with business forms and customs, may 
draw up his own contract if he prefers to run the chance of 
doing it properly. 

In case the farmer, alone, or associated with others, de- 
sires to do his own work, and with his own rig, then the 
choice of methods and rigs enters into first place and the 
matter of contract is eliminated. 

KINDS OF MACHINES. As previously stated, no state- 
ment of general preference will be risked. Each class of 
machines has its special advantages or is undoubtedly the 
best under ceitain circumstances. The conditions of drilling 
here, however, differ from those of most other sections. OlS 
eastern drillers declare work here to be far harder than work 
in the east where the rock is more solid, where the casing 
may be omitted in many or most cases, and where the 
formations are better known and understood. Here the 
formations are principally shale and the drilling very diffi- 
cult and heavy casing always necessary. 

POLE MACHINES. The earlier wells in Dakota were all 
drilled by pole rigs, that is, rigs using wooden drill-rods. 
Aside from the matter of time taken up in the coupling and 
uncoupling of the rods in putting the tools into, and taking 
them from, the well, these rigs have proved most satisfacto- 
ry under all circumstances and have, without doubt, per- 
formed the best, cheapest and most rapid work. 

The uncoupling of the rods or their breaking are disad- 
vantages which tend to frequent accidents but these risks 
are largely overcome by the use of efficient grappling tools 



12 

The special advantages of the pole rigs lie in the certainty 
of their drilling action. The revolution of the rods is uni- 
formly in the direction of tightiiing the screw threads of the 
joints, thus aiding in preserving the tightness of all the con- 
nections. Again— the rods forming a rigid connection be- 
tween the drill and the hand of the driller, the action and 
position of the drill is under perfect controU. If the rods 
turn it is certain that the drill turned also and that the hole 
is being drilled circular and not oblong. In this certainty of 
control over the action of the tools lies the chief great advant- 
age, in this state, of the pole rig over all others. Again— the 
rigidity of the string of poles makes it possible to tell exact- 
ly where the bottom of the hole is and to better con troll tne 
blows of the drill. This advantage tends further to an in- 
crease in the number of blows delivered per minute for the 
rods have greater weight than the cable ond sink more rap- 
idly, the friction of their smooth surfaces is less than with 
the corrugated surface of a cable and the rigidity makes it 
certain that if the upper end of the string of rods sinks that 
the lower end has done the same— there being no kii.k, i»r 
bending, or looping, as with a cable. 

CABLE MACHINES. Cable rigs; that is, rigs using eith- 
er rope or wire cables in the place of drill rods, are very large- 
ly used now because, principally, of the facility of operation. 
In letting down the tools and in removing them much time 
is saved by having a continuous run instead of having to 
stop every thirty feet to couple or uncouple a rod or pole. 
The danger due to the uncoupling of a joint is done away 
with, In these features lie the chief advantages of the cable 
rig. The disadvantages are many and well worth consider- 
ing. The danger of breaking the cable, under strain, or if a 
tool becomes fast, is greater than with poles. The cable is 
rotated both to the right and to the left thus making it pos- 
sible to readily uncouple a joint at the tools, if, perchance,, 
the joint became loose by the jar of the drilling. There is. 
danger that the rotation of the cable will not always cause 
a corresponding rotation of the drill and the hole not be 
drilled truly circular thus causing trouble in sinking the 
pipe. This is especially noticablein the important operation 
of reaming, w^hich is the enlargement of the hole by scraping 
away its sides, an ope-ration requiring care and a tool so 
worked as to cut away the full circle and not merely part of 
it. With the cable the rotation may have the effect of mt^re- 
ly twisting the rope instead of rotating the tool. With the 
pole rig this cannot be. Again, when the hole is several hun- 
dred feet deep, and where the drilling is done in Avater which 
may be flowing out with considerable velocity and pressure, 
the velocity of the drill blows must be slow. If the motion is 
rapid the walking-beam returns to the lifting motion before 
the tools have had a chance to fall and drag down the cable 
against the upward motion of the water. 



13 

In this way the energy expended may be absorbed not 
in effective drilling but in merely churning on the cable. 
With poles this is otherwise, as explained. On occount of 
these manifest disadvantages several drillers have abandon- 
ed the use of cables in the drilling work and have construct- 
ed what are called "combmatioii'' rigs, that is, rigs using 
poles for drilling and the cable for operating the sand pump, 
and for other purposes requiring rapid action. This ar- 
rangement has proved most satisfactory for it combines the 
advantages and eliminates the disadvantages of both -sys- 
tems. There may, in the cable rigs, be a choice as to cables. 
Jn most cases the 2 inch r©pe is used because it is cheaper 
than wire, but the wire possesses the advantage of answer- 
ing all the conditions of stength required in heavy service, 
and, it is said, the elasticity of the wire, w^hen under the ten- 
sion of the life, aids materially in the important operation 
of twisting the drill, thus, to a great extent, neutralizing the 
effect of possible carelessness on the part of the driller. 

HYDRAULIC OR JETTING MACHINES. 

These rigs are of many patterns and workon quite dissim- 
ilar plans but all pass by the common name of "jetting" 
or "rotary" rigs. In one class of rig the drilling is done 
with a very short drill-bit having a hollow shank through 
which a jet of water is forced from the hollow drill rods 
(pipe-rods.) This creates an upward current which car- 
ries out the drillings, thus doing away with much pumping 
and permitting the almost continuous operation of the drill. 
These rigs are almost untried here but much is claimed for 
them. 

The rotary hydraulic rigs are among the latest in the Da- 
kota field and hence are the most untried. They have in 
other sections, and especialy in the shallower wells proved 
vastly superior to other rigs. In several cases here they 
have had phenmoinaily successful runs, down to depths of 
500 to 700 feet, but for greater depths they have not proved 
a uniform success, yet the process could not, in most cases, 
be blamed for the failure. 

Judging from the very flattering successes met with in a 
few cases, one may safely predict a very wide field of use- 
fulness for these machines, and especially when their oper- 
ation in our peculiar formation is better understood. Even 
these rigs— like both the pole and cable rigs— are already 
undergoing the ordeal of rearrangement and modification to 
better suit them to the conditions here met. The lastest ad- 
vices are to the effect that very important modifications 
have but recently been made, by the American Well Works, 
which promise to make the rig as nearly suited to Dakota 
as mechanical ingenuity can at present approach. 

The elements of watchfulness, mechanical ability, quick 
and accurate judgment, and, above all, extreme care neces- 



14 

sary to success with any rig or any system apply particular- 
ly to this class of rigs. 

It may be said (as the result of ten years of exper ence 
and observation in Dakota) that a very large majority ol the 
many accidents in the well-drilling operations of this state 
have been due, not to any fault in the process or the rig, but 
to sheer ignorance or 'carelessness on the part of the 
drillers, many of whom have been without knowledge of, or 
experience in, the well business, hired as mere helpers yet 
placed, often times, m full charge of the work and with no 
responsibility as to its safe and proper conduct 

This being undeniably true, it may be further stated that 
the exercise of care and judgment is of more importance 
to the owner of a rig than the mere mechanical details of 
the rig itself; for a poor tool, in the hands of an expert, loill 
do better icork than a fine tool, in the hands of a careless 
and ignorant loorkma^i. 

TOOLS. 

In the selection of drills, reamers, pumps, grappling- 
tools and other accessories of a drilling outfit select with 
reference to the size and style of the rig, and in matters 
of detail rely upon the advice of some responsible manufac- 
turer; bearing in mind one thing — get enough tools. Do not 
work "short handed," for it will not pay in the well business. 

If a rod or cable breaks, or a tool is dropped into the well, 
be prepared to handle the case AT OXCE, for any delay 
may cost hundreds of dollars. Have the tools to treat all 
cases, have them where they belong, and don't allow a meal, 
a circus or even cold or darkness to interfere with prompt 
action and invaribly leaving the work so it is safe. 

Be prepared for accidents for tliej' are sure to come ! 

The machinery having been selected, and the well begun, 
the next consideration is as to the pipe. 

PIPE. 

LAP'WELD. The selection of a suitable pipe is a 
matter of importance upon which de- 
pends, very largely, the success or the 
failure of the well. In the past, pipe of 
.all sorts of makes and weights has been 
jused, and with varying success. 

Wrought iron pipe is of two classes — 
the BUTT-WELDED and the LAP- 
WELDED. Fig. 1 shows the great differ- 
ence between these welds, and the super- 
BuTT-W£LD. ior strength of the lap-weld which h s 
Fig. 1. about 4 times- as much surface in contact 

at the weld as is had in the butt-weld. 

It is clear that butt-welded pipe would not be safe to use 
in our wells, yet some has been used and with disastrous 
effect. 




15 

All pipe should be lap-inrelded . 

The thinner the pipe the sliorter and weaker is the weld; 
the thicker the pipe the longer and stronger is the w^eld. 
Wrought iron pipe (like most other things these days,) is, in 
its different classes, made on standard models; i hat is, the 
thickness, area, weight, etc., per i'oot. for any given size will 
vary but little -as between different makers, and certain 
standard brands are listed by nearly all. Thus, there is 
what is known as "Standard" pipe, x or extra strong, xx or 
double extra strong, casing pipe, line pipe, drive pipe, tub- 
ing, etc. 

Most of these brands will not be used here. The standard 
pipe is that which is commonly used and is a brand suffici- 
ently heavy for every use unless it be that of very heavy 
driving for which purpose drive-pipe is designed, it being 
©f a better grade of iron and hence stronger. For lighter 
work— as for the casing used in starting a w 11, or the pipe 
used in recasing an old well— the lighter or casing pipe is 
the grade used. 

Table No. 1, on the next page, gives the dimensions, 
w^eights, etc., of "Standard" pipe. 

Some drillers are of the opinion that drive pipe should be 
used in all Dakota well work because of the liability of get- 
ting the pipe fast and being obliged then to subject it to 
very heavy driving, or pulling with jack-screws, in order to 
loosen it. There is, of course, much ground for this opin- 
ion and it goes without proof that if the stronger pipe* is 
used the well will be the better for it and the operation of 
sinking it the safer; but it were useless to use heavier pipe if 
a lighter grade would answer every purpose. 

The opinion is, therefore, repeated that if the drilling and 
reaming are properly and sufficiently done, tlie "standard" 
grade of pipe will serve every purpose, at any rate in wells 
of 8 inches or less in size. The wear and tear on the pipe is 
greatly lessened by sufficiently reaming out the hole under 
the pipe, by the use of expansion or other reamers. Fre- 
quently this is overlooked, or insuffiiently done, and the 
pipe, after hard driving, becomes fast and days, or even 
weeks of delay are consumed in an effort to loosen it and to 
do over again what should have have been done well in the 
first place. Too great care cannot be used m this part of 
the work. If the reaming is w^ell done the pipe will settle 
easily and rapidly, or with but light driving, and a lighter 
grade of pipe might safely be used; but if the reaming is in- 
sufficiently done, and heavy driving resorted to, then stand- 
ard or drive pipe should be used. 

It shauld be noted that the external diameters of pipe 
must remain the same in order to fit to standard couplings. 
If the pipe is made heavier ♦^he extra metal is added to the 
inside and the intern al diameter thereb y reduced. 

*Drive and line pipes are of standard sizes and weights, but being of a 
better grade of iron they are stronger and more expensive. 



16 
TABLE NO. 1. 

READIA'G IRON COMPANY. 



ai s;a3)ao3 



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O M mo roo rOM rotnt^ONriO O OnOn" O w 

O O O M IN -^O OnnO lt.nO On"1W w^o 0\" OOO rot-. 

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oocooooooocooooooooooooooo 



•jooj 



ro N M invo oo ■»*• ^~ ro t.. looo ^ r.« oo t^ m 

■4- IN vo -* « t-. u^ a\NO t^->fiOCT'*^>OH-.*-t-..Tt- 00 

N'^LOOOM^OPlVONOC^U^O^fOu^C^'^mOVO C\ 

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TOO J oiqno 

-noo 9di J 
JO q}3u3i 



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lO ro f> -<J- C4 M 
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d d O d d d w pJ CO -^ c^ On N m 0-03 oo" d ^cd m i-o 




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t^NO ON PI 01 Tfoo wnOnOnO TCP) o tcno oj 00 O '-I O 
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rt o 

^ m 

c c 

O O 

a 



u 



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ai 


H 


u 


rr 


u 


Pi 


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c 


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rt 


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T1 


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TABLE XO. 2 

RE.IDTXG IROy COMPANY. 



STANDARD. 



Wrought Iron Lap-Welded Pipe, 

FOR STEAM, GAS, AND WATER. 



MANUFACTURERS' PRICE LIST. 
REVISED AND ADOPTED SEPT. 18, 1889. 

To take the place of all previous lists and subject to change 
without notice. 



Nominal 


Price 


Price 


Nominal 




No. of 

Thread per 

inch of 


Inside 


per Foot, 


per Foot, 


Weight 


Thickness. 


Diameter. 


Plain. 
$ c. 


Galvan'z'd 
$ c.~ 


per Foot. 




screw. 


IncHes. 


Pounds. 


Inches. 




I>^ 


•23 


.26 


2.68 


.145 


"X 


2 


•30 


•34 


3.61 


.154 


iiK 


2>^ 


.4.7 


•53 


5.74 


.204 


8 


3 


.62 


.68 


7-54 


.217 


8 


ZV2 


•74 


.88 


9.00 


.226 


8 


4 


.88 


1.03 


10.66 


•237 


8 


A'A 


1.06 


131 


12.34 


.246 


8 


5 


1.28 


1.60 


14.50 


•259 


8 


6 


1.65 


2.00 


18.76 


.280 


8 


7 


2.10 




23.27 


.301 


8 


8 


2-,75 




28.18 


.322 


8 


9 


3-75 




33-70 


•344 


8 


lO 


4-75 




40.06 


.366 


8 


II 


6.00 




45.02 


•375 


8 


12 


7.00 




49.00 


•375 


. 8 


13 


8.00 




5400 


•375 


8 


14 


9-50 




58 00 


•375 


8 


15 


11.00 




62.00 


•375 


8 



Prices of Standaixl Pipe. 

Discount on galvanized pipe about 55 per cent. 
" " plain " " 62^ " " 

(See table No. 3.) 

The same prices are quoted by all makers and as the mar- 
bet price fluctuates the rate of discount changes. Current 
discounts can be had from the makers. Those given here- 
in are not the latest but will fully answer the purpose of ap- 
proximate estimates. 

For selected pipe, or pipe cut to special length the dis- 
count is usually 5 per cent. less. 



18 



TABLE NO. :^. 

The following prices are also quoted, 
NET PRICES. 



Size of pipe. 



lYz inches. 
2 

2% 

3 

31/2 

4 

41/2 

5 

6 

7 

8 

9 

10 

12 



Tubing. 


Line pipe. 


Drive pipe. 


.12 
.14 
.19 

.28 






..12 
.17 

.21 

.26 

.30 

.36 

.44 

.56 

.72 

.90 

1.30 

1.55 

2.30 






.28 


.39 


.40 






1 


.76 


1 




1.20 






1.95 
2.53 




1 



Standard pipe. 



.O81/2 

.1114 

.17% 

.2214 

.21% 

.33 

.3914 

.48 

.m% 

.18% 
1.07 
1.401^, 

1.78 
2.62 






This table is arranged so as to show comparative prices of 
different grades of pipe. The prices for standard pipe being 
the net prices vesulting from the discount and list prices 
given in table 2, for plain pipe. 

The prices here given will fully answer the purpose of es- 
timate. Exact prices can only be had by correspondence 
with the manafacturers, who will quote the latest lists and 
discounts. 

That feature of the pipe which is of the greatest consern 
to the well driller is the thread and it is chiefly on account 
of the thread that heavier pipe is needed. If the pipe is thin 
and light so much of the body of the metal is cut away in 
the operation of threading as to leave a thin shell not suffi- 
ciently strong to withstand the driving blows without dan- 
ger of stripping the thread. 

If the pipe is heavy the body of metal back of :^he threads 
is stronger and the pipe therefore more able to withstand 
heavy work. 

COUPLINGS. (See table No. 7.) 

The common form of coupling is straight threaded, that 
is, the line of the ttireads is parallel to the outer surface of 
the coupling. An improved form gives greater strength to 
both pipe and coupling and distributes the strain more even- 
ly over the line of the thread. This is known as the patent 
TAPER COUPLING. From the illustrations of this form 
of coupling, shown in connection with the advertisements 
on the front and back covers and by Fig. 2 on page 20.. it 
will be seen that the inner face, or threaded surface of the 
coupling, has the form of a funnel to fit a corresponding 
conical taper on the pipe. In drive-pipe the ends of the 
pipe meet at the middle of the coupling. 



19 
TABLE NO. 4. 

READIX'G IRON' COMPANY. 



X STROiNG AND XX STRONG 

Wrought Iron Lap-welded Pipe. 

X STRONG. 





Price 
per Foot. 

5 'c. 


Actual 


Nominal 




Nominal 


Size. 


Outside 


Inside Th 


ickness. 


Weight 




Diameter. 


Diameter. 




per Foot. 


Inches. 


Inches. 


Inches. I 


Qches. 


Pounds. 


IX 


.46 


1.90 


1.494 


203 


3-63 


2 


.60 


2.375 


1-933 


221 


5.02 


^% 


•94 


2.875 


2315 


280 


7.67 


3 


1.24 


350 


2.892 


304 


10.25 


1% 


1.48 


4.00 


3-358 


321 


12.47 


4 


1.76 


4-50 


3.818 


341 


14-97 


^% 


2.12 


5. 


4-25 


35 


17.60 


5 


2.56 


5-563 


4.813 


375 


20.54 


6 


330 


6.625 


5-750 


437 


28.58 


7 


4.20 


7.625 


6.62 


50 


37.60 


8 


550 


8.625 


7-50 


56 


47-85 



XX STRONG. 





Price 
per Foot. 


Actual 


Nominal 




Nominal 


Size. 


Outside 
Diameter. 


Inside 
Diameter. 


Thickness. 


Weight 
per Foot. 


Inches. 


% c. 


Inches. 


Inches. 


Inches. 


Pounds. 


^y^ 


.92 


1.90 


1. 088 


.406 


6.40 


2 


1.20 


2.375 


I.49I 


-442 


9.02 


2^ 


1.88 


2.875 


1-755 


.560 


13-68 


3 


2.48 


3.50 


2.284 


.608 


18.56 


Z% 


2.96 


4.00 


2.716 


.642 


2275 


4 


3-52 


4-50 


3 136 


.682 


27.48 


aYi 


4.24 


5- 


3-56 


.72 


32.45 


5 


5.12 


5-563 


4.063 


•75 


38.12 


6 


6.60 


6.625 


4.875 


.875 


53" 


7 


8.40 


7-625 


5.98 


.82 


60.34 


8 


11.00 


8625 


6.88 


.87 


71-52 



Discount about 62^ per cent. 
Not the most recent quotation. 



20 



TABLE NO 


5. Ci^SlNCx, NET 


PRICES. 




Nominal 




Actual 


Nominal 


No. Threads 


Inside 


Price 


Outside 


Weight 


Per Inch 


Diameter. 


' Per Foot. 


Diameter. 


Per Foot. 


of Screw. 


3i 


20 


3? 


4.27 


14 


^i 


21 


3I 


4.60 


14 


J4 


24 


4 


5-47 


14 


4 


25 


4i 


5.85 


14 


4i 


27 


4i 


6.00 


H 


4i 


35 


4i 


9.00 


14 


4i 


30 


4l 


6.50 


14 


4? 


36 


4l 


9.00 


14 


4t 


33 


5 


7.58 


14 


5 


35 


5f 


8.00 


14 


5 


41 


5i 


iooo 


14 


5 


48 


5i 


13.00 


lU 


5 


58 


5i 


17.00 ■ 


Hi 


Si^ 


39 


S^ 


8.50 


14 


5& 


50 


5i 


13.00 


Hi 


i)8 


45 


6 


10.00 


14 


5t 


50 


6 


12.00 


Hi 


5f 


55 


6 


14.00 


"i 


H 


59 


6# 


II. 15 


14 


H 


64 


6f 


13.00 


14 


H 


74 


6| 


17.00 


Hi 


i 6| 


68 


7 


1300 


14 


! 6f 


78 


7 


17.00 


Hi 


' 7* 


83 


8 


15.00 


Hi 


7l 


95 


8 


20.00 


Hi 


8i 


95 


81 


16.15 


Hi 


81 


1.05 


81 


20.00 


Hi 


8i 


I 15 


8t 


24.00 


Hi 


8t 


1. 00 


9 


18.00 


Hi 


9f 


125 


10 


21.00 


ni 



10 inch Light Pipe for Well Purposes Net, 1.50 

As made by the Oil Well Svipply Co., Pittsburg, Penn. — See advertisement 
Fig. 2 shows sections of pipe joints and the patent taper coupling re- 
ferred to on P. IS. Fig. 2. 




PATENT SLEEVE COUPLING. 
FLUSH JOINT. INSERTED JOINT. 



21 

EXPLANATION OF PIG. 3. 




Main pipe of well. 

Gate valve. 

Hand wheel to valve. 

Cro.ss, the openings of 
which may all be of one 
size or may all be differ- 
ent. State sizes desired. 

Plugs, for closing dead 
openings. The tops may 
vary as shown. 
Bushing, for reducing size 
of openings. 

Nipples, for connecting 
specials, being short piece 
of pipe threaded part way 
or all the way and being 
of any length desired. 

(.^urved tee, just the form 
for top of pipe. Especial- 
ly where well is used for 
power. 

Plug, plugged for gauge. 
Pressure gauge. 

Reducer. 

Elbow, can be had to any 
angle. 

Double elbow. 

Straight tee, can be had 
of any form or rize. 

Reducing tee, can be had 
of any form f)r size. 



Fig. ;l Specials and fittings for pipe. (See page 29. j 

TABLE NO. 6. 

TABLE OF COMPARATIVE WEIGHTS OF DIFFERENT KINDS OF WBOUGHT 

IROX PIPE. 



Size of Casing Standard I X. j 
pipe. pipe. , pipe. Strong P.' 



2 
3 

4 

4K 
5 

5M 
6 

7 

m 

8 

^% 
9 

^% 
10 

10% 



Drive pipe. 



2.23 
3.95 
4.27 
5.33 

6.00 
7.25 

IM 
8.08 
9.35 

10. or, 

12.45 



3.61! 
5.74| 
7.54j 
9.00 
10.66| 
12.341 



3.63| 
7.67! 
10.25i 
12.47' 
14.97 
17.60 



14.50i 20.54 



18.76; 28.58 



13.50 
15.10 
16.15 
17.25 



20.00 



23.27 

28! is 

'33!76 



37.60 



Drive pipe is of standard 
Aveight and size but more expen- 
sive, stronger and better on ac- 
count of its being made of a bet- 
ter quality of iron. Then, too, 
the threads are cut longer to fit a 
longer and stronger coupling (see 
table 7 1 and of sufficient length 
to permit the ends of the pipe to 
Ijutt together when coupled — 
this it not the case in standard 
pipe— thus very greatly adding to 
the strength of the pipe in the 
operatitm of heavy driving, the 
pipe being i)racticaUy continous 
and not separated at each joint. 
This is the distinguisliing fea- 
ture of drive pipe. 



8ize— outside diameter, weights— pounds per foot. 



22 



TABLE NO. 7. 

Dimensions of Wrought Iron Couplings. 



FOR STAXDAED PIPE. 



Inside diam. 
of the pipe. 


2 


214 


3 


3'/2 4 


41/2 

0{k 


7, 


6 


7 ,8 


9 


10 


Outside dia . 
of coupling. 


271 


9 


! 

4 i 4411 5x^ 


7/s 


8y 


9-!8 


10|§ 


ll§i 


Length of 
coupling. I 2% 


31/8 


3f6 


3%: 3M 


We 


s% 


31/2 


4 


4 


6tV 


6^ 



FOR LINE PIPE, DRIVE PIPE AXD TUBING. 



Inside diam. 
of pipe. 


2 


21/3 


3 


31/2 


4 


4^2 


5 


6 


7 8^9 


10 


Outside dia. 
of coupling. 


031 
-^32 


m 


4t^s 


m 


51/8 


5M 


6M 


7M 


....! 9j% ; 


iiM 


Length of 
coupling. 


s% 


m 


m 


4 


4 


4^. 


4H 


434 


1 

.... -Ai 


6ife 



FOR CASING PIPE. 



Inside diam.i 
of casing. 2 


21/2 


3 


m 


4 


41/2 


5 


0% 


6^4 


6| 


m 


8V4 


Ouiside dia. 

of coupling. 2M 


3M 


m 


ii^ 


4|| 


0% 


5% 


6^ 


7H 


Til 


8% 


9% 


Length of 
coupling. ; 2% 


3^8 


3x^5 


3A 


3| 


31 


3?8 


3^2 


_i.^^ 


4tV 


-trV 


-iT% 



TABLE NO. 8. 

Dimensions, &c. of Soecial, Lap- Welded, 

KALAMEIN PIPE, 

for water and gas works, 

As made by the National Tube Works Co., Chicago. 



Outside 
diam. 


Weight of 
lock joint. 


W^eight of 
lead, one side. 


Nominal 

weight per foot 

complete. 


Aproximate 
price per foot. 


Inches. 


Pounds. 


Pounds . 


Pounds . 


$ Cts. 


2 


4 


1 


].80 


.17 


3 


8 


m 


3.35 


.30 


4 


12 


2^ 


5.00 


.42 





17 


3^ 


7.15 


.55 


6 


21 


5 


8.60 


.67 


7 


30 


6 


11.25 


.87 


8 


33 


^Vs 


12.80 


1.00 


9 


38 


"U 


15.10 


1.25 


10 


40 


8 


16.60 


1.45 


11 


m 


lOK 


20.:^5 


1.70 


12 


56 


n% 


24.50 


1.87 


13 


65 


12K 


27.60 


2.25 


14 


71 


13M 


30.00 


2.50 


15 


100 


151^ 


36.40 


2.80 


16 


120 


17 


46.25 


3.30 



28 
TABLK NO 9. 



TABLE SHOWING RELATIVE AREAS 


OF STANDARD PIPE. 


Size 

of 

Pipe. 


% 


1 


m 


2 


2>2 


3 


3'4 

21.70 
12.20 
5.44 
3.06 
1.96 
1.81 
1.00 


4 

28.10 
16.00 
7.11 
4.00 
2.56 
1.77 
1.30 
1.00 


5 

44.4 
25.00 
11.10 
6.25 
4.00 
2.77 
2.04 
1.56 
1.00 


6 


7 


8 


1 

1% 

2 


1.00 


1.77 
1.00 


4.00 

2.25 
1.00 


•7.11 

4.00 
1.77 
1.00 


11.10 
6.25 
2.77 
1.56 
1.00 


16.00 
9.00 
4.00 
2.25 
1.44 
1.00 


64.00 
36.00 
16.00 
9.00 
5.76 
4.00 
2.93 
2.25 
1.44 
1.00 


87.10 

49.00 

21.70 

12.25 

7.84 

5.44 

4.00 

3.06 

1.96 

1.81 

1.00 


113.70 
64.00 
28.40 
16 00 


214 








10 24 


3 










7 11 


314 












5 22 


4 














4 00 


5 
















2 56 


6 








.... 










1 77 


7 




















1 30 


8 






















I'jDO 



From Wm. -J. Baldwin, M. E. in "Steam Heating for Buildings." 

Explanation of table: The relative areas of any two 
sizes of pipes given in the table will be found at the inter- 
section of the horizontal and vertical lines representing the 
given sizes. Thus, a 6-inch pipe = 1.00 6-inch pipe, 1.44 5- 
inch pipes and 4 3-inch pipes; an 8-inch pipe = 4 4-inch 
pipes, 16 2- inch pipes, 113.7 ^^-inch pipes, etc. 

Application— It is desired to supply 50 three quarter inch 
pipes with a constant flow, what size of supply pipe should, 
be used ? Take top horizontal line and run to the right, it 
will be seen that a 5 inch main will supply but 44.4 
inch pipes; but a 6 inch main will supply 64.00. 
pipes, hence, a 6 inch pipe must be used. An 8 inch well is 
as large as 7.11 three inch wells, a 7 inch well as large as 
3.06....4 inch wells. 

As to Relative Dircharging Powers of Pipes, see Table 
No. 27. 

TABLE NO. 10. 

AVEIOHT OF STANDARD OAST IRON PIPE. 



% inch 







(Including Bowl and Spigot ends.) 






Casi 


L iron weighs 450 lbs. per cubic ft. and .2604 lbs. 


per cubic inch. 


Diam. 


W^ eight per foot for following thicknesses. ' 


Length 










Pipe. 


Vz 


% 


% 


H 


f'8 ! % 


% 


1 


Feet. 


2 


3 


6 


9.3 


14 


-19 , 






8 


3 


4 


9 


13 


18 23 1 29 






12 


4 


5 


11 


17 


23.5 30 t .37 


44 


52 


12 


5 


6.0 


13.5 


21 


29 ; 36 : 45 


53 


62 


12 


6 


8 


16.5 


25. 


34 


43 53 


63 


73 


12 


8 


10 


21.5 


32.5 


44 


56 i 68 


81 


93 


12 


10 


14 


27. 


40.5 


55 


69 84 


99 


114 


12 


12 


15 


32 


48 


65 


82 100 


117 


135 


12 



As made by Addyston Pipe & Steel Co. (See adv't P. 216.) 

This table incudes all of the sizes and weights likely to 
find a place in water and gas works plants In Dakota, where 
the use of cast iron for water w^orks is on the increase. 

(See also the advertisement of Dennis Long & Co. P. 217.) 



24 
TABLE yO. 11. 

DIMENSIONS, PRICE, ETC., OF SPIRAL RIVETED PIPE. 

No. 18 Wire Guage. Thickness .049 inch. 







Price, tar- 


Price per 


Approx. 


Approx. 


Diam. in 


Price per 


red and 


ft. Galvan- 


weight per 


bursting 


inches. 


ft. Black. 


asphalted. 


ized. 


100 feet. 


pressure 




NET. 


XET. 

If .19 


NET. 


lbs. 


lbs per sq in. 


3 


6 .17 


$ .23 


185 


1300 


4 


.21 


.23 


.29 


245 


1000 


5 


.25 


.28 


.35 


300 


800 


6 


.29 


.32 


.43 


360 


700 


7 


.32 


.35 


.45 


400 


600 


8 


.37 


.40 


.52 


460 


500 


9 


.41 


.45 


.59 


525 


450 


10 


.45 


.50 


.65 


575 


400 


11 


.48 


.53 


.70 


625 


360 


12 


.58 


.64 


.82 


750 


330 


13 


.62 


.69 


.90 


800 


300 


14 


.67 


.75 


.98 


900 


280 


15 


.75 


.83 


1.05 


950 


260 


16 


.80 


.88 


1.13 


1000 


250 


18 


.88 


.96 


1.28 


1125 


220 


2U 


1.00 


1.10 


1.45 


1250 


200 




1.10 


1.21 


1.55 


1350 


180 


24 


1.20 


1.32 


1.67 


1460 


160 



In lengths of 25 feet and less, with plain or crimped ends. 
As made by Abendroth <k Root Mfg. Co. (See adv't P. 238.) 
The weights given are for the black pipe, other grades are from 10 to 20 
per cent, heavier. 

This class of pipe is very extensively used in the west for 
conveying irrigation waters, and in many places for water 
works use. Its strength is very great while the weight is 
very light, and the cost low. On account of its strength, 
lightness and cheapness it will be especially adapted to use 
in Dakota, where water must be piped on or near the sur- 
face. 

The following table will show the comparative weight of 
the three classes of pipes— Spiral, Standard wrought iron 
and Cast iron: 



Heaviest Spiral 
Pipe. 



W^EIGHTS. 

Standard Wrought 
Iron Pipe. 



Cast Iron 
Pipe, % inch 



. 2H 
.5 



3 inch 2 lbs . 

4 

6 

8 
10 
12 
14 
16 
18 
20 
22 
24 



...8 

..10 

. . 13 

..15 

..18 

...20 

...22 

..24 

.26 



71/2 lbs 13 lbs 



10% 

18% 

28 

40 

49 

58 



.17 

.25 

.32 
.40 
.48 
.56 
.64 
.72 
.79 



.95 



Pipes of this class in California have been in use since 1853 and have 
given great satisfaction, many having done useful service for 25 and 30 
years. 



25 
TABLE NO. 12 



READING IRON COMPANY. 



c/5 


English 
gavige in 
fractions. 


u 

c 


* Jti< ' _!« • • • • hf, • • • • 

. ^» . 1" . . . . T* 





_j^ C in 


j3 


s 

►— 1 


O\NirvN00ir>N OOvO'sJ-N O\00 t^ m -^ . . . 

q q q q q q q q q q q q q q q q q q . . . 


LU 

or: 

00 

a 

z 

Q 
z 

< 

z 

< 

CJI 

2 

UJ 

< 

PL 


S c ""* 
.y 4) 

in "I'S 
S 2 u 



c 


• • |cq • • • • M 

. > i« . . . . n«> 


£ rt S 
<5 M^ 


J3 


e 
1— 1 


Tl-rorONNNNwNHi-ii-ii-itHi-iOOOOO 

q q q q q q q q q q q q q q q q q q q • • 




00 On '-' N fO ■<:h "^vO t^OO ON "-I N ro ri- i/^vo t^ 00 


J3 S '^ 
en'" C 

bo Wl-^ 
C =! 


■J 




bO v/ - 
C 5 u 


"o 


TT LT) -^ OnOO ro "^OO -^ On vr> fO N moo 
io<^iOO -t ^ toroM OOOvO Tj-roN O OnOO r^v£) "^ 
T}-Tj-rofOroriNMNM>Hi-(Mi^i-ii-iOOOOO 







m 

N 

(75 


a C en 
rt— c 
y 4) 

« 3 y 

fi a! rt 




Q 

Q 
z 


e 

C 1> C 
4> M.S 
C 3 
^ rt « 


J3 


C 
p— 1 


vO 00 00 r^vO 'd- fO On fO t/^ ^ ONt^OO ON >-4 00 N 

ON'^'^ONr^ONrt-i-i n Tj-00 Tr»*00»-''^t^Ow^ 

nOOnONOOvoNOOOvO-^NnhO OnOO t^vO 10 u^ Tf 

Tt- Tf ro fo c< N N N w M w w w HN q q q 


< 







OoRO'^^'^'^ ^^^ t^OO On f N fO Th tovO t^ 

§0° MMI-,W«M«M 



26 

Inadvertently the text lor this page was overlooked but 
two suggestions may be here inserted with profit, no doubt, 
to some. 

The first suggestion is prompted by the abundant rain-fall 
of the early months of 1892 which has been tar greater than 
that of any former year within the history of the state. 
Some are heard to say that "irrigation will now be overlook- 
ed." Such will not and should not be the case, for, al- 
though 1892 may be a year of great productiveness without 
irrigation, it will still— however good it may be— fall far 
short of accomplishing what irrigation would accomplish. 

Through any given series of years Dakota's rain-fall can- 
not be relied upon to be sufficient for remunerative farm- 
ing ; so irrigation must be resorted to by all who desire cer- 
tainty of return for each season's labors. If all who can 
will, during this favorable season, prepare for the unfavor- 
able seasons which are sure to come, they will exercise wise 
forethought by hastening to improve the opportunity so 
fortunately offered of preparing in advance. This promis- 
ing season' will no doubt aid many financially to in whole or 
in part prepare for irrigation in the future. 

It is said of an Arkansas farmer that he refused to mend 
his leaky roof during fair weather because it was not neces- 
sary, and during foul weather he couldn't because it was 
wet. It is hoped that our farmers will not emulate such un- 
thrif t by refusing to prepare for irrigation during wet sea- 
sons, because it is then unnecessary, and being compelled to 
put it off during dry seasons because too poor. 

A second suggestion will be risked, although somewhat 
outside of the scope of this work. It is: 

t>o not he deceived by so-called Rain Makers ! Do not fol- 
low so intangible a will-o-the-wisp as this latest ''fake" with 
which scheming sharpers are attempting to delude the peo- 
ple. The U. 8. government spent several thousand dollars 
in a vain attempt to produce rain; an attempt which was an 
acknowleded failure, except that it awakened in the breasts 
of certain shapers an idea which they have enshrouded in 
mystery, and on the strength of which they seek to extort 
money from a too credulous public. Eain-making has not 
been a success as yet— we hope it may be in the future. 

Water we have below us. We know it is there, and that 
we can get it. Seek it, therefore, and do not delay in the 
vain hope that the secret of rain-making has been vouchsaf- 
ed to men of whom the world has never heard, men un- 
known in the sphere of science, men whose investigations 
were never heard of and whose successes are but hearsay or 
newspaper reports, men who want pay in advance and will 
not exhibit the powers which they claim thus suddenly to 
have acquired to the light of scientific investigation; men 
who work in the dark and who seek their own interests and 
not yours. Some wit has wisely said that, as yet, "the har- 
ness-maker is the only successful rein maker." 



8" 



27 

SPIRAL WELDED PIPE. 

This pipe is very similar to the spiral riveted pipe, the 
joint being welded instead of riveted. The weights are 
about the same as the weights of riveted pipe, but, by reason 
of the welded joint, the pipe is claimed to be stronger, more 
durable, smoother internally. Both possess the same great 
advantages of lightness and cheapness and are equally well 
adapted to use in irrigation whenever a light, durable and 
inexpensive pipe can be used. (See distribution of water, 
P. 122.) 

From the foregoing tables it will be possible to select a 
quality or kind of pipe suited to the needs of the well, the 
water-works plant, or the conveyance of water over the 
surface for irrigation . More detailed information maybe 
had by correspondence with the manufacturers or dealers in 
pipe whose advertisements appear herein. 

The proper grade of pipe having been selected, the plan of 
the well must be decided upon, for it may be on several 
plans. 

A large outer casing may be first used and sunk as deep 
as thought desirable, then a smaller size sunk inside of the 
first, and, possibly, still a smaller size within the 
second pipe; the latter being carried to the bot- 
tom. The two outer pipes may then be pulled 
up, leaving a continuous pipe from top to bot- 
tom. In some cases, as where the outer casing has 
become fast and cannot be lifted, the outer pipe 
is left in the well thus making a double string 
of pipe. In other cases, all the outer casing is 
removed, but 2 or 3 lengths, the space between 
the two casings being then calked. 

In some wells the telescope plan is used. In 
this case the well may start with an 8 inch pipe 
carried down say 300 feet; then a 6 inch pipe is 
carried down say 400 feet lower, or to a depth of 
700 feet, and, by the use of a left-handed thread 
at the 300 foot level, the upper 300 feet of the 6 
inch pipe is removed, leaving the lower 400 feet 
in the well as permanent casing. In like 
manner a 43^ inch pipe may be sunk within the 
six inch pipe and carried to water; the upper 
700 feet being then removed. Such a well, in 
section, would have the appearance shown in 

Fig. 4. 

Most of the earlier wells were of this class 
and many are still drilled on this plan, but the 
practice now appears to tend more in the direc- 
tion of wells with a continuous line of pipe from 
top to bottom, and such wells no doubt have 
many marked advantages over wells of other 
classes. 



4" 



Fig. 4. 



28 



(f''^/. 




PERFORATED PIPE. 

Nearly all of the northern wells throw out more or less 
shlae mud, clean sand, or lumps of sand-rock or iron pyrites. 
These hard bodies have, in city water systems, caused much 
trouble by clogging the lire nozzles or water pipes. To pre- 
vent the throwing out of such masses many wells have been 
filled with lengths of perforated pipe dropped to the bot- 
tom of the well. The lengths of pipe thus inserted are per- 
forated with 3^ or % inch holes 
which, while admitting the water 
or sand, prevent the admission of 
the larger solid bodies. The conse- 
quence of thus shutting off free 
access to the well is that large quan- 
tities of loose rock accumulate 
about the base of the pipe, as shown 
in Fig. 5, thus gradually shutting off 
the water supply and diminishing 
the volume and efficiency of the 
well; besides which, the effective 
erea of the base of the well pipe is 
reduced by the insertion of this 
smaller pipe thereby still further 
decreasing the capacity of the well. 
Additional disadvantages of this 
p. 5 inserted pipe lie in the fact that it 

Showing a perforated pipe IS out of reach and control, it be- 
in the bottom of a well, comes a loose and independent feat- 
ure of the well, not under control or subject to needed re- 
pairs, and it is apt to become out of line with the main pipe 
—if not entirely disconnected from it— thus forming a pos- 
sible and unmanageable obstruction at the base of the well. 
If the perforated pipe is left out, the well, at the bottom, 
will be clean and free to receive whatever comes to it. If 
rock is thrown, care for it at the sruface where it may be 
collected and disposed of. Put in a settling reservoir to re- 
ceive it, or, in case of water works, where the pressure 
must stand in the pipes, run the water through a large sand 
drum which will collect the heavy matter and permit only 
the water and lighter sediment to pass to the mains. 

It is, indeed, safer to collect the rock at the surface, where 
it may be cared for, than to permit it to accumulate at the 
base of the pipe where it cannot be cared for and may ruin 
the well. 

If the well becomes stopped up by an accumulation of 
sand or by other causes the pipe may be more easily cleaned 
out if it has a uniform diameter from top to bottom and it 
is unobstructed by the presence of a section of loose perfor- 
ated pipe. Usually the services of a well driller will be 
needed to open up a well which has become clogged. The 
objections urged against the use of perforated pipe in wells 
are not founded on theory alone but upon actual experience 



29 

in a number of the more important wells of the state. 
VALVES, HYDRANTS AND SPECIALS. (See Fig 3p 21) 

Every well should have at leist one gate valve in order 
that it may be shut off in whole or in part, for otherwise no 
control could be exercised over the flow by the person in 
charge. 

The kind, of valve to buy is a matter of importance, for 
all are not equally good, either as to pattern, workmanship, 
or material. Of the many makes of valves the Ludlow and 
the Chapman are among the best and are the most used in 
the Dakotas. (See adv't Chapman Valve Co., P. 210; of the 
Ludlow Valve Co. P. 224; of the National Tube Works Co. 
front cover; of the Brass & Iron Works Co. P. 225; and of 
Robinson & Cary Co. P. 242.) 

The greatest care is necessary in the selection of a hydrant 
for water works service. Almost any hydrant will v( ork 
well in clear water but few, however, will prove satisfactory 
in case sand or gravel is held in suspension by the water. 
A hydrant having a rubber or leather face or cone will need 
frequent repairs, owing to pieces of sand or gravel becom- 
ing imbedded in the soft surface. These, too, tend to wear 
the surface of the metal ring, and thus leaks are caused and 
the hydrant frequently freezes and becomes unserviceable. 

Where there is much grit in the water a metal faced hy- 
drant should be selected. Where the water is clear the 
others will prove as good. A gate valve should, be handled 
carefully. Do not close it suddenly for the "Water Ham- 
mer," due to the sudden checking of the velocity of a rapid- 
ly moving column of water, under heavy pressure, is very 
great and tends to injure the pipe and its connections. 

The arrangement of the valve, or valves, will depend upon 
the circumstances surrounding the well and its uses. 

Usually the main valve is placed horizontally on the main 
pipe and all connections are made above the valve. In this 
position the valve is usually put on before the main flow of 
water is struck, the drilling being continued throiigli the 
opened gate— care being taken to protect the face plates of 
the valves by a thin nipple set into the top of the well. If 
the valve is not set until after the flow is struck much loss 
of time and money may result before it is finally set to the 
pipe against the force of the flow. (A notable instance of 
this was that of the first "city well," at Aberdeen, where it 
was found to be impossible to set the valve because of the 
force of the water, and hundreds of dollars were wasted, and 
special tools finally constructed, before the water was flnally 
shut off and the valve set.) 

This danger may not be ever present, especially in the 
smaller wells, but reference to it will call attention to its 
consideration. Sometimes a cross is set first, on top of 
the pipe, before the flow is struck. It is then an easy mat- 
ter to set the gate to the top or the side opening, the stream 
finding a partial outlet, meanwhile, through the other open- 



30 

ing. After the gate is set the other openings may be plug- 
ged or otherwise connected. 

If the main gate— or any gate valve — is set on any line of 
horizontal pipe, leading from a well throwing any sand or 
solid matter, the valve should be set vertically, that is, with 
the hand-wheel at the top. This will prevent sand or stone 
lodging in the w^orking parts of the valve; a danger which is 
ever present if the hand-wheel is at the side of, or under- 
neath, the pipe. 

Whatever may be the location of the valves, or the use to 
which the well may be put, one thing should be observed, 
w^hich is, so arrange the specials (which is understood to 
mean the crosses, tees, valves and such similar features of 
the pipe fittings) as to leave a vertical opening above the 
main pipe, which opening may be closed by a plug if not 
otherwise connected. 

By so doing ready access to the well is alw^ays possible, 
for the purpose of cleaning out, blowing olf, or other pur- 
pose, without disturbing the other connections of the well. 

If the well is to be used for power, in the running of a 
mill or other heavy plant, much power may be saved by 
using long curved specials instead of the short, right-angled 
specials commonly used. Every well driller ought to have, 
as a part of his outfit, a full set of specials (crosses, tees, ys, 
nipples, bushing, plugs, elbows and a pressure guage) so 
that, on the completion of a w^ell, a sufficient test of its pow- 
er and volume could be made to be of value as a matter of 
public record and also as a matter of value to the driller 
himself, who would, through the wide publicity given to all 
such systematic tests, derive a direct benefit, in the way of 
advertising sufficient to pay him for the expense and time 
invested. 

The more such matters are observed the more will public 
attention be called to our artesian wells and the more quick- 
ly will capital be attracted. Properly viewed, it would be a 
wise stroke of business policy for every well owner and con- 
tractor to interest himself in these features of a well and to 
be prepared to put them to efficient tests. 

Even the well owner cannot aiford to be without the few 
specials necessary to a proper control over his well, or to its 
direction in such manner as may best suit his varied needs. 
Supposing the well to be 6 inches, what ought to be provided? 

1 — 6-inch cross. 

1 — 6-inch tee. 

1 — 6-inch elbow. 

2— 6-inch plugs (one plugged for attachment of gauge.) 

2 — 6-inch nipples. 

2— 4-inch " 

2— 2-inch " 

1 nest of bushing for 4-inch and 2-inch connections. 

1 pressure gauge. 

With these few specials the well, or any connection with 



31 

it may be reduced or directed as occasion may require. At 
least these specials should be obtained. 
LOCATION or WELL. 

As a rule, a well for irrigation will be located on or near 

the highest point of land to be irrigated, but considerations 

of convenience or economy may, at times, suggest a location 

at a lower point or near one's buildings from which location 

the water may be piped to the higher ground. 

The reservoir will usually occupy the highest ground and 
the well may be placed at the most accessible point near it 
or at such a point as will best conserve the proper division 
of the fields or the location of the ditches. All of these 
things should be considered and mapped out before either 
the well or the reservoir is located; otherwise the location 
may, in the end, prove to have been badly chosen. 

At whatever point the well is located let that point be 
OUTSIDE OF THE RESERVOIR. Some wells have been 
located within the reservoir where they are not accessible 
because of either water or mud, where, in case of needed re- 
pairs, it would be difficult to convey the machinery and sup- 
plies, or to erect or handle the same, where the well cannot 
conveniently be used for anything else but to supply irri- 
gation waters and where its flow could not be easily regu- 
lated during the winter months. 

If located outside of the reservoir the well would be ac- 
cessible at all times and subject to control; it could be easily 
repaired or opened up — if stopped up; — its volume could be 
first used as power to run machinery, a revenue, possibly, 
being derived from the rental of the power, and the water 
then conveyed to the reservoir by a short pipe. It could be 
enclosed and protected from the weather as every well 
should he in order to protect and preserve the pipe and 
valves from rust, for the well is but a piece of machinery 
and should be cared for as such. It will wear out in time by 
rust and wear and will need recasing, but in order to pre- 
serve it as long as possible, its pipes should be painted and 
protected. If thus cared for it will last intact for many 
years and pay for itself many times. The cost for repairs 
being almost nothing. 
LOG OF WELL. 

Section 35 of the -'Melville" law provides that the con- 
tractor of any township well shall keep a log of the well, or, 
in other words, a record of the successive strata through 
which the drill passes. From the very nature of the case 
this must be a dead-letter, for it cannot be enforced. 

The driller may report such a log as he chooses, and no 
one else be the wiser. The truth is, it is safe to say, that no 
properly recorded log has ever been made of a Dakota well. 
The author has seen many wells drilled, and has carefully 
noted the methods adopted, but in only one case, within his 
knowledge, was there anv eifort made to obtain an accurate 
log. 



32 

Dozens of records have been published in papers pam- 
phlets and reports, but all are subject to grave doubt, as to 
truth or accuracy. Some drillers will make no report — pre- 
fering to keep, as a trade secret, whatever they may have 
discovered— but most drillers pay no attention to the drill- 
ings, and, except for the fact that at one depth the drilling 
is hard and slow, and at another depth it is softer and more 
rapid, they know little or nothing about the character of the 
formations in which they have worked. 

The keeping of a log involves considerable extra labor, 
systematic watchfulness, a certain degree of knowledge of 
geology, and, above all, a certain amount of expense to 
which the contracting driller does not care to go. He agrees 
to drill a well, and not to instruct in geology, and, to him, 
the drillings discharged are all the same. 

It must be admitted that a carefully kept log, or rather 
series of logs, would be of much value, but how to secure 
them is a question each driller alone can decide. Certainly 
section 35, above referred to, can result in nothing more 
than a succession of false reports which will be worse than 
none at all. When the first well in the state was drilled, 
(the Ry. well at Aberdeen) by Mr. Swan, the author was 
present daily and assisted in keeping the log, preserved sam- 
ples of the drillings, dried and arranged them, and finally 
mounted them in 3-foot glass tubes secured for the purpose. 

If equal care was used with each well the logs would then 
approach the truth and possess some value. Each owner of 
a well should look to it that this is done. 

Equally important — yes, far more important— is the keep- 
ing of an accurate record of the performance of each well, 
and as to all its dimensions, thus — depth and log, and length 
of each size ot casing in well. Size at top or bottom, or all 
the way. 

Pressure — "When closed, and when flowing from openings of different 
sizes. 

Volume — When open full and when throwing streams of different sizes ; 
not guessed at but carefully measured Avith a weir. 

Discharge — Exact height of stream thrown vertically when well is opened 
full, and from openings of 1, 2, 3, 4. 6 or 8 inches. Also, the ex- 
act distance these streams will be thrown horizontally. 

Temperature of the water. 

Whether hard or soft, clear or sandy or muddy. 

The exact time occupied in drilling the well, with dates. 

The quality of pipe used. 

The kind of machine used in drilling. 

The exact cost. 

There is nothing in the above form of record that cannot 
be kept by any farmer or driller and nothing that is not of 
importance or that cannot be determined if only a few spec- 
ials are at hand. The measurements of volume and height 
of streams are simple operations and are fully explained 
herein. (See measurements by weirs.) See— how to meas- 
ure the height of a stream, page 93.) 



A series of records kept as above suggested would have 
value, but the records as heretofore kept have but little. 
Even the published, official records, or reports, are far from 
accurate. A record, once carefully made, ought to be pre- 
served for future reference, for the memory alone cannot be 
relied upon. 
DRILLING. 

Little need be said under this head for it is assumed that 
an expert will be in charge of the work. If an inexperi- 
enced hand is in charge he has more to learn than a book of 
this size would hold. A few suggestions, however, will be 
in order. 

Do every part of the work thoroughly and with the greatest 
■ care. L'se great care in handling tools about the pipe 
so as not to drop them in. 
Make every joint of the rod or the tools fast so they will 

not loosen, and cause the loss of a rod or tool. 
Keep the drills and reamers in proper cutting order, and 
inspect everything frequently to see that nothing is loose 
or defective. 
Do not work the drilling tools too Jong before pulling out, 
for it is better to pull out more frequently, and make sure 
that everything is safe and sound, than to attempt to work 
longer and lose a tool by reason of a loose joint. 
Above all, do the reaming well, so that the pipe will settle 

easily and not stick or require heavy driving. 
Keep the pipe pretty close to the bottom, in order to avoid 
the caving in of the walls or the inrush of quick sands 
and the possible sticking of the tools. Many drillers will 
run from 20 to 100 feet without settling the pipe, and they 
usually have trouble in consequence. Only room enough 
is needed below the pipe to work the drill and the reamer 
and usually the length of a single section of pipe will be 
ample. 
Do not sink a smaller hole below the main hole, for it may 
endanger the latter work by causing the drill to stick or 
drill a sloping hole into which the pipe cannot be forced. 
Never leave a tool standing in the well, for a cave-in may 
bury it and render its extrication difficult if not im- 
possible 
If any accident happens do not cease labor until it is reme- 
died or until its remedy is seen to be impossible. 
Arrange in advance for all supplies, in order that no delay 
may endanger the continuation of the work. A "shut 
down" often sets the work back more, and causes greater 
expense, than though no work had been done. 
Always leave the work in a safe condition and protected 
from the depredations of the curious and thoughtless on- 
lookers. 
< Cautions might thus be indefinitely extended— each found- 
ed on some costly experience of the past — but enough has 
been suggested to show the necessity of an exercise of such 



34 

a degree of care and watchfulness as is required in but 
few other callings. If no accident happens the driller de- 
serves much praise. If one does happen he usually has 
himself to blame. 
COST OF WELLS. 

Many thoughtless enthusiasts have raised the cry that 
wells ought to be drilled for from $1,200 to $2,000 but such 
persons are not authorities and do not know whereof 
they speak. The cost of a well depends not upon one thing, 
but upon many things. The size is, of course, the chief 
factor for the pipe for a large well will cost more than that 
for a small well; the rig used must, as a rule, be heavier; 
the tools heavier; the coal and water used will be much 
more; and the labor bill will be much greater because th^ 
drilling will take longer. The location of the well will 
effect its cost. If within the limits of a town, having a 
system of water works so that the water used in drilling 
may be readily secured (and under pressure), the otherwise 
large water-hauling bill will be saved. If the well is on a 
farm, or where no water is at hand, the hauling bill will 
mount to most respectable proportions. 

Add to these items the cost of moving the rig to its site, 
setting it up and taking it down, hauling the pipe and fuel, 
to say nothing of the many certain yet unforseen incidental 
expenses and you have the well driller's bill of expense, 
minus the ever-present chance of an accident which may 
cost hundreds of dollars or result even in his financial ruin. 
No man of good business judgment will assume these 
risks for the mere chance of earning day's wages. He 
claims, and is fairly entitled to receive, a generous compen- 
sation for the risk he assumes, and, in addition to that, such 
wages as his skill as a driller entitles him to receive. 

Eor the purpose of illustration the following approximate 
cost is given of a 6 inch farm well 1,000 feet deep: 

1000 feet of 6 inch pipft @ .62 per foot $ 620 

Frieght — at reduced rates about 50 

Hauling pipe to the ground '• 40 

" casing pipe away " 10 

" and transporting rig " 50 

Setting up rig " 150 

Taking down rig, and breakage " 100 

Fuel, and hauling same " 250 

Hauling or obtaining water '• 100 

Wear and tear on rig and tools " 200 

One gate valve " 30 

Couplings " 40 

Interest on investment for 90 days " 75 

Labor bills @ $10 per day for 60 days " 600 

Total " $2,315 

In this estimate it is assumed that but 60 days are con- 
sumed in the work of moving, setting up, drilling and taking 



35 

down; that there are no accidents or unusual expenses and 
no delays. 

The incidental expenses could not safely be figured at less 
than $300, and most of the other items given are figured too 
law; so that, without any allowance for incidentals, accidents 
or profit, and allowing but three men on the work, and but 
60 days of time, the expense still exceeds $2300 for a 6-inch 
well. It is not the intention to throw any unfavorable 
light on the matter of cost of wells, but rather to throw on 
the true light, and, by calling attention to the details, dispel 
some false light. 

A well is worth all it costs, 
and the driller must have some show as well as the owner. 
A 6-inch well costing from $3000 to $4000 is cheap, if prop- 
erly put down, and is a grand investment, and one which is 
better, at that price, for the farmer than for the driller, for 
where the driller may make $500 or $1000 profit on one well 
he may lose it all on the next; whereas, the farmer with the 
well has a sure thing and a competency. 

Any well will pay its cost in 5 years— whatever the cost 
may be — or at the rate of 20 per cent, on the investment. 
ISome wells have paid for themselves in one year. 

If a farmer has a well which enables him to raise even 30 
bushels of wheat to the acre, in a dry year when his neigh- 
bors fail to get back their seed, and he has but 140 acres un- 
der water, he receives 4,200 bushels, which, at but 50 cents 
per bushel, nets him $2,100, or suflicient to pay for a well 
large enough to thoroughly irrigate his 160 acres. This is 
not overdrawn but underdrawn as based upon actual expe- 
riences. One well, in 1891, more than paid its cost by garden 
irrigation, and, besides this, supplied water to the towm . 

Many such examples could be given to show how service- 
able a well is and how short a time it takes to return its 
cost. Nor need one seek a dry year in order to show the 
contrast, for even in the best years the service of a well is 
so great as to make the increased yield pay very largely on its 
cost. 

It may be asked — what do your Dakota wells cost ? The 
answer would be difficult to frame for lack of proper infor- 
mation and knowledge of all the facts entering into the 
matter of cost. Wells 4|or i% inches have cost from $1,800 
to $3,000. Wells of 6 inches from $3,000 to $7,000; although 
about $3,000 is the common price. VVells of 8 inches have 
cost about $4,000 or $5,000. The expensive wells have, in 
all cases, been expensive by reason of delays and accidents. 
As drillers have become more skilled in this field, and rigs 
have been adapted to its formations, the price of wells has 
been reduced, and a still further reduction may be expected 
as skill and competition increase. The cost of a Dakota 
well ought to be considered in connection with its volume. 
The mere hole has no value; it is the water which it supplies 
on which a value is placed. 



36 

The hole costs so much, regardless of the volume of water 
thrown out, so that if two wells cost $2000 each, and one 
well throws out 1000 gallons per minute, while the other 
throws out but 500 gallons per minute, it may be fairly said 
that one well cost twice as much as the other, for the one 
supplies but half the service of the other, or has cost twice 
as much for a given return. So, too, as between Dakota 
wells and those of other sections of the country. 

The Dakota artesian basin is the largest and the greatest 
in the world and the volumes and pressures of its wells 
greater than the volumes and pressures elsewhere. So it 
may be said that it costs far less here to get a given volume 
of water than it does any where else in the world. This ba- 
sin is the nearest to the manufacturers of well machinery, 
pipe, tools, and other supplies which therefore cost less. 
The depths are but moderate, and the volumes enormous, so 
that the duty or service received for the money expended is 
greater than in any other section or country. 

In Australia many wells are put down by the government 
at a cost of from $5,000 to $25,000, yet their best wells do 
not equal the average Dakota wells. Our farmers may 
therefore deem themselves most highly favored by nature 
and ought not to grumble at the expense of obtaining water, 
for, by no other system, and in no other section of the 
world, can an equal volume be obtained for the same 
amount of money. No reasonable man will complain of ex- 
pense when he pays far less than the balance of mankind 
and when all the conditions are so favorable for the speedy 
return of the money invested. 

Nor will any wise investor hesitate to put his money into 
Dakota wells or farm lands when the conditions, as they are 
here, are shown to him in comparison with the conditions 
elsewhere, under which conditions tens of millions have 
been invested to the great profit of the investor, prosperity 
of the settler, and glory of the state and nation. 

It must further be considered that the cost of the water 
is but a part of the cost of the land. The well is of no val- 
ue except as it supplies the water; the water is of little val- 
ue except as it feeds the ground and aids in producing a 
crop. The cost of land, well, ditches, reservoirs and 
other improvements could properly be "lumped," and the 
total value per acre found. In this, as in the cost of the 
water alone, Dakota will be shown to hold the palm as 
against the world. This matter will be more fully consider- 
ed under the head of land and water values. 

Some have asked— how can I get a well the cheapest ?— by 
contracting with a driller, or by buying a rig (either alone 
or by clubbing together with my neighbors) and doing my 
own work. Many reasons prevent a reply. Firstly, iusffici- 
ent data as to what has been done heretofore renders a reply 
impossible, or, at best, purely speculative. Secondly, the 
outcome will depend upon who you are, what your means 



37 

may be, what your general intelligence may be, and espec- 
ially as to the amount of natural mechanical ability you 
may possess. Many farmers could not drill a well with the 
best of tools. Some ingenuous farmers have actually drilled 
good wells with rigs and tools of their own make. iSafety 
and economy would appear to lie in the selection of a con- 
tractor who has the tools, knows the business and is prepar- 
ed to assume all risks. It is to be hoped, however, that 
hundreds of rigs will be purchased by farmers, and that we 
may soon evolve a race of practical drillers from among our 
own people. 
ARTESIAN WELLS, ELSEAVHERE. 

It is within a comparatively short time that artesian well 
waters have been used for irrigation in this country, but 
their value is now being appreciated and thousands are be- 
ing sunk for this purpose. As above stated, there has not 
yet been discovered in the world another artesian basin of 
such extent as the Dakota basm nor one whose wells possess 
such great volume and pressure. 

Artesian wells are common to nearly all of our states and 
to most countries and some few wells have been drilled 
that compare very favorably with the better Dakota wells 
but they are few in number and widely separated, and the 
artesian basins thus far discovered are of but moderate 
area. The Dakota sand-rock formations extend far to the 
south so that Nebraska and Kansas have a few good wells 
but most of the southern wells are shallow and the flow but 
weak. 

A group of 5 we)ls at Coolidge, Kansas, cost an average of 
S400 each and have an average flow of 25 gallons per min- 
ute. A like ratio between cost and volume would make a 
Dakota well of 1800 gallons cost S16,000, whereas there are 
several throwing a greater volume the cost of which has 
been from |3,000 to $4,000. The smaller wells of the Crook- 
ed Creek Valley, numbering about 100, and costing only 
about $20 each are used for irrigation and about 50 of these 
serve from 5 to 25 acres each. 

A new artesian basin has but recently been discovered in 
Washington, in the Yakima valley, where there is one well 
flowing 650,000 per day or 452 gallons per minute. This 
would rank among the smaller wells of Dakota. A com- 
pany has been organized to drill wells throughout this new 
field wherein hundreds of thousands of dollars have been 
expended in irrigation development by other systems and 
where, within a decade, a barren, sage-brush desert has been 
made the home of the peach and the prune, and the heart of 
a vast and prosperous agricultural interest. 

In Colorado several thousand wells have been drilled to 
depths ranging from 100 to 1800 feet, but in most cases to 
depths of from 300 to 700 feet. The w^ater from many must 
be pumped but in most other cases the flow ranges from 10 
to 75 gallons per minute. 



38 

The town well at Anamosa has a flow of 495 gallons per 
minute. This is the largest of over 2000 wells in the San 
Louis valley, Bucher's well, at the same place has a pres- 
sure of 25 pounds to the square inch. The Espinosa well, 
about 20 miles north of Monte Yista, according to the re- 
port of the state engineer, " throws a solid three-inch col- 
umn of water nearly 40 inches above the casing, and flows 
between 300 and 400' gallons per minute." 

Compare this pigmy, which thus deserves special notice 
in Colorado, with such Dakota gushers as the Aberdeen, 
Huron, Eedfleld, Doland, Columbia, Wjponsocket, Spring- 
field and Yankton wells not to mention' a host of others 
each of which would be a marvel in any other land. 

In California there are 25 artesian basins of varying char- 
acter and pressure but that of Kern county is the most re- 
markable and more nearly resembles the Dakota basin than 
any other yet found. Its area is only about 18 by 14 miles 
and it has an elevation of about 300 feet above the sea. The 
average depth of the many wells in this area is about 500 
feet. 01 these wells 54 range in flow from 150,000 to 
4,000,000 gallons per day, or from 100 to 3,000 gallons per 
minute. 

One wells has a volume of 3,000 gallons per minute, two 
wells flow 2,100 and 2,400 gallons, nine wells flow from 1,400 
to 2,000 gallons, and seventeen wells flow from 700 to 1,400 
gallons per minute. The diameters range from 6 to 10 
inches. 

The counties of Tulare, Los Anseles and San Bernardino 
have also remarkable artesian basins and hundreds of very 
fine wells from 150 to 500 feet in depth. About 4 miles 
south of San Bernardino is the Gage group of 29 wells, all 
within the radius of a mile, the average volume being about 
389 gallons per minute, and the average depth but 150 feet. 

In other parts of the United States there are many nota- 
ble wells and artesian basins, as there are also in China, in 
the Sahara desert, and in nearly all of the countries of 
Europe, especially in Germany and in France. The scope 
of this little book will not, however, permit their considera- 
tion.' It is suflicient to note that the artesian well is of 
world-wide interest to mankind but it is in Dakota that the 
great wells may be saidto be at home. 
DAKOTA WELLS. 

The pioneer well of Dakota was begun in the summer of 
1881, at Aberdeen, by the Chicago, Milwaukee & St, Paul 
Ry., for the purpose of supplying water for its engines. 
The well was drilled by Mr. Swan, and, by reason of changes 
in the size of pipe, and unavoidable delays, the cost was far 
greater than it would otherwise have been. The flow was 
struck early in the spring of 1882, at a depth of 920 feet. 
The pipe was 6 inches at the top and 43^ at the bottom. 
The volume was not accurately measured at the time but 
a very close approximate measurement placed the volume at 



39 



1,200 gallons per minute and this increased later on to over 
2,000. The pressure ranged from 150 to 180 pounds to the 
square inch. The 6 inch pipe was carried to a height of 70 
feet and, from a 2-inch nozzle at the top of this pipe, a 
stream was thrown 60 or 70 feet into the air against a 
gentle breeze.* 

Encouraged by the success at Aberdeen, other wells soon 
followed throughout the length of the territory until, today, 
they stretch over an area of over 400 miles north and south 
by over a hundred miles east and west, and the limit of the 
field in any direction has yet to be found. 

A complete list of Dakota wells could not be given for 
lack of information, but a list is given below of a few typic- 
al wells which may be taken not as exceptional wells select- 
ed for the purpose of parade but as purely representative 
of the wells in all parts of the state— such wells as any 
farmer in the state can get if he will but try, and wells 
which, when once obtained, will be to the owners a mine of 
wealth such as few at present dream of. 

TABLE NO. 13. 

KEPEESENTATIVE SOUTH DAKOTA ARTESIAK 

WELLS. 





ToAvn 


Depth 


Bore 


Flow 


Pressure 


County. 


or 


in 


in 


in gals. 


in B)sper 




Location. 


feet 


inches. 


per min. 


sq. in. 


Aurora 
Beadle 


Plankinton 
Huron weU 


750 
862 


6 

5% 


1000 
1668 




""m" 


" 


'• Day" 


840 


4 


476 


120 


.( 


■' Risdon'" 


960 


5% 


2250 


175 


u 


Hitchcock 


960 


4&3 


1240 


155 


Brown 


Aberdeen, Cy 


908 


5^8 


1800 


180 


" 


" Sewer 


1000 


6-41/2 


1215 


155 


u 


•' Beard 


1050 


6&5 


1000 


138 


" 


Columbia 


966 


W2 


1:B99 


160 


Bon Homme 


Springfield 


592 


8 


3293 


80 




TyndaU 


735 


41/2 


552 


45 


Douglas 


Armour 


725 


41/2 


700 




Hand 


Miller 


1145 


3^2 


462 


100 


Hughes 


Harrold 


1453 




150 


40 


Marshall 


Britton 


1004 


41/2 


601 


120 


Sanborn 


Woonsocket 


725 




5000 


153 


" 


" 


775 


7 


7000 


150 


Spink 


Ashton 


900 


4 


750 


100 


" 


Mellette 


910 


4V^ 


1215 


165 


•' 


Redfleld 


964 


41/2 


1261 


166 


'• 


Doland 


897 


41/2 


710 


112 


" 


Baker well 


920 


41/2 


2000 


165 


Yankton 


Yankton 


610 


6 


1800 


56 


" 


>( 


610 


6 


2200 


50 



The author compiled the above table from previously published re- 
ports and has made such corrections as were possible. The figures given, 
are, in the main, correct. 



*This is the first accurate account published as to this first 
well. The record was made by myself at the time and has 
been carefully preserved. The record published by State 



40 

Engineer Coffin was erroneous, having been obtained, no 
doubt, from parties who were not properly informed. Sim- 
ilar errors appeared as to otlier wells, as to which 1 am ac- 
curately posted. The official reports ought to be as accur- 
ate as possible and none but the best authorities accepted. 
It is difficult, however, to attain to great accuracy in this 
matter. Maj. Coffin deserves praise for attaining so nearly 
to it. W. P. B. 

The Dakota artesian basin, as stated, is of unknown ex- 
tent. Wells are found throughout the length of the two 
Dakotas and far northward into the British possessions, as 
they are also to the south through Nebraska, Kansas and 
Texas. On the east the field appears to terminate within 
the borders of the state, where first appear the quartzite for- 
mations. (Certain evidences are adduced by Maj. Y. Y. B. 
Coffin, ex-state engineer, to prove that even within the 
quartzite area wells may be found, and that the true limit on 
the east is in Minnesota where the truearchaean formations 
appear. To the west is a domain as unknown as it is vast. 
If the supply of this basin, as supposed, comes from the 
mountains of Wyoming and Montana, then it would be 
possible to find wells at all points between the Missouri 
river and the mountains except within such areas as have 
been affected by igneous uph'eavals or other geologic dis- 
turbances. 

It is sufficient, however, to know that on any section with- 
in this broad basin, extending for over 400 miles north and 
south by about 100 miles east and west, a well may certainly 
be had. The water bearing formation is the Dakota sand- 
rock, a formation of unknown thickness m this field al- 
though of vast thickness in its far "western out-croppings. 

The southern wells of the state penetrate this formation 
at a depth of about 600 feet. The formation dips thence to 
the northward until, at Jamestown, on the Northern Pacific 
it is over 1400 feet below the surface. The dip appears to 
be comparatively uniform so that it is possible to determine, 
within very close limits, at what depth water will be struck 
at any point. 

Overlying this soft, porous, water-bearing sand-rock there 
is usually a thin stratum, or cap-rock, of harder sandstone 
or limestone. Above this the formations are principally of 
blue and gray shale with occasional strata of sand or lime- 
stones. It is the drilling in these shale formations that is 
so difficult, tor, as stated by some drillers, the shale seems to 
pack like putty or lead and does not mix readily with the 
water used in drilling. 

Much has yet to be learned as to Dakota w^ells, as to the 
formatioms to be penetrated, as to the relationship— if any 
there be— between volume and pressure and as to the source 
and the volume of supply, and, especially as to the best and 
cheapest way of drilling wells, the best machinery or process 



41 

to use and, above all, the best use to be made of the water 
after it is obtained. The Dakota farmer has also to learn 
how to use the water so as to get out of it the highest duty, 
when to use it on different crops and in what quantity on 
different soils and during different seasons. A grand work 
is well begun, and our larmers have but to labor and gain 
dollars thereby, while the scientist speculates upon the mar- 
vels of nature as they develop and gains knowledge from 
his speculsitions. 

Under the head of Water, and of Reservoirs, will be found 
several tables relating to the duty of well waters. The vol- 
umes of wells, volumes thrown per minute and per day and 
volumes per minute equal to given volumes per day, vol- 
umes thrown in one and three months by wells of different , 
volumes per minute, volumes required to cover different 
areas to different depths and time required by different 
wells to do it, equivalence of cubic feet and gallons and 
of gallons and cubic feet, equivalence of other units of 
volume or measurement, and other tables of value relating 
to wells. 

The sequence of our subject requires that the Water fol- 
low the completion of the well, so that " Water, its pro- 
perties, measurement," &c will next be briedy considered; 
after which will be a brief consideration of the matters of 
storage by reservoirs and its distribution by ditches, flumes 
and pipes. 

COPIES OF THIS BOOK 

FOR SALE BY 

W, p. B^TLIH, 

Ahevdeen, South Dahota, for 25 cents. 

Also sets of detailed drawings of gates, outlets, flumes, 
weirs, and similar constructive details of an irrigation 
plant. These drawings could not be inserted, in this book. 
Price per set 25 cents. 



42 

WATER. 

Its Properties, Duty and Measurement, with tables of 
Weight, Pressure, Volume, Discharges, &c &c. 
Miscellaneous Notes. 
Pure water is composed of Hydrogen and Oxygen. 

By weight, ll.l 88.9 Parts. 

By measure , 2 1 " 

Its greatest desity is at a temperature of from 39.2° to 

39.8° from which point it expands by either heat or cold. 
It boils at a temperature of 212 % and freezes at 32° Fahr. 
Evaporates at all temperatures. 
Is but slightly compressible. 
Is not palatable when pure or distilled. 
Wieght— See P. 62 & 63 Tables of weight, and notes 

appended. 
Weight— See P. 61 " " " on one acre. 

Pressure — See P. 64 " " pressure. 

" of column per sq. in. = height of column X 4.331. 
" " *' " circ. in. = height of column X .3369. 

Press, of 1 R) per sq. in. is exerted by column 2.311 ft. high. 
Volumes— See tables under head of Mensuration , and fol- 
lowing tables. 

A cu. ft. of saturated air at 50° contains 4.09 gr's. of water. 

A cu. ft. of saturated air at 55° contains 4.86 gr's. of water. 

A cu. ft. of saturated air at 60° contains 5.79 gr's. of water. 
A fall of snow of 11 inchesis equal to about one inch of 

rain, but this varies greatly. 11 inches being for a dry snow 

not drifted . 

Depth of water in in's. X 2,323,200=cu. ft. per square mile. 

Depth of water in inches x 3,630= cubic ft. per acre. 

The "CENTER OF PRESSURE" is ^ of the depth from 
the surface- Thus, in a reservoir or tank 12 feet deep the 
average pressure on the sides will be found at a point 8 
feet below the surface. The amount of this pressure is 
equal to the depth of this point x by 62)^ (the weight of 
1 cu. ft. of water). In this case 8 ft., the depth, X 623^= 
499 pounds = the average pressure per sq. ft. on the entire 
surface. To get the total pressure on the sides multiply 
the total area of the sides by the average pressure, as 
above found. The total pressure on sides and bottom = 
3 times the weight of the fluid contained in the tank or 
reservoir. 

The pressure on a sluice gate, in the bank of a reservoir, 
2x3 feet and the center 8 feet b low the surface of the wa- 
ter in the reservoir=8x 62 1^=499 lbs. per foot; 2x3=6 sq. 
fi. X499= 2994 pounds, or nearly 1% tons. 

The daily supply of water per capita In cities having water 
works systems ranges from 45 to 17o gallons, and averages 
about 75 gallons. In nearly all cases the per capita de- 
mand increases from year to year. 

Water presses towards an orifice from all directions and 
diminishes the volocity it the proportion of about 63 to 
100; or the quantity delivered through the orifice will be 
less in this proportion than the calculated amount. 



43 
DUTY OF WATER. 

By the duty of wafer it is meant the amount of duty or 
service it will perform, or the extent of its usefulness in 
any given field. 

Considered as a power, it is so many horse power for a 
given volume under a given head. Considered as an irri- 
gating medium its duty is the number of acres a given vol- 
ume will adequately serve ; or, as it is usually stated, the 
duty of a second foot is so many acres. That is to say, a 
volume of one cubic foot per second, fiowing constantly 
during the irrigation season, will serve a given number of 
acres. 

This element of duty is not, of course, a subject of exact 
measurement for too many variable elements enter into its 
determination to render this possible; yet the duty may, in 
any particular section, be very clearly estimated. What the 
duty will be will depend altogether upon the crop to be 
served, and the nature of the sub-soil and surface soil on 
which the crop is grown. 

The duty in one state will differ from the duty in another 
state, as will the duty in one section of a state differ greatly 
from that in another section of the same state. One crop 
will require more water than another, or the same crop may 
require more water on one soil than on another. 

In Dakota little is known as to the duty of water for, as 
yet, no measurements have been made, no extended system 
of irrigation is in practice and little thought has yet been 
given to this matter; nor has any effort been made to arrive 
at the maximum duty of any one well. When the township 
well system becomes general, and the greatest service, or 
duty, is demanded of each well, then will carefully kept re- 
cords of duty be required, and such records will form the 
basis of estimates which will closely approximate to the duty 
of the well waters in the several sections of the state, and 
lead to a knowledge of better methods of application and 
conservation of the supply. 

Kor is duty a constant quality for it is constantly on the 
increase; that is, the duty increases from year to year — oth- 
er things being equal— the ratio of increase being very rap- 
id immediate!}' after the installation of the system of irri- 
gation This is apparent on considering that when the 
water is first applied its volume is very largely absorbed in 
placing the soil in proper condition. This having been done, 
the same volume will, the next year, serve to supply the 
prepared area and still leave a surplus for the reclamation 
of a further area. 

So, each year, the field of duty is extended until the max- 
imum is finally reached. As stated, the duty in any locality 
will depend very largely on the nature of the soil, and it will 
depend still more upon the mean rain fall over that section. 
In a locality, or during a year, where the precipitation is 
small and nearly the full necessary supply must be artifici- 
ally supplied the duty will be low; but where the precipita- 
tion is nearly suflicient to supply the needs of agriculture, 



44 

and but a small portion need be artificially supplied, then 
the duty will be high. 

In considering, therfore. what the probable duty in Dako- 
ta will be, account must be taken of the character of the 
soil, the comparative precipitation and evaporation and the 
nature of the crop. 

Hon. J. S. Greene, state engineer of Colorado, in the 1888 
report states, as an approximate estimate, that the precipi- 
tation on the mountain areas west of the great continental 
divide is 33 inches, and on the plains areas 10.7 inches; an 
average over the whole of that area of 25 inches. Also that 
on the mountain areas east of the divide the precipitation 
is 30 inches, and on the plains areas 15 inches; or a total 
average of 18.7 inclies. He states further, and, in this, is in 
accord with other authorities, " that the limit of remmiera- 
tive farming, without irrigation is draton at an annual 
prerdpitation of tioeaty-two inches,'"' that is, if the precipi- 
tation Is less than 22 inches there cannot be certainty as to 
a remunerative return for agricultural labor. The matter 
of distribution of this precipitation enters here as a matter 
of the greatest importance as shown by the example cited 
on page 92. 

In this report it is further stated, with reference to the 
duty of water and the distribution of precipitation — "as 
there is a demand for general results in this matter, it may 
be stated, relative to the duty of water on the plains of Col- 
orado, measured where distributed to the land, that one sec- 
ond foot, running throughout the irrigation season, in addi- 
tion to about 5 inches of ram-fail during April and May, 
and 4.5 during June, July and August, if distributed with 
fair care to diversified crops, on what might be called aver- 
age land, would irrigate from 60 to 70 acres. It is noticed 
that, to accomplish this duty, it must be measured where 
placed upon the land. This is not always considered when 
speaking of the duty of of water. " (P. 406.) 

Referring to table 14, below, it will be seen that the pre- 
cipitation during April and May, in Dakota, has equaled or 
exceeded 5 inches in past years, except during 1890 and 1891; 
and that, in every year the precipitation during June. July 
and August has exceeded 5 inches, so that the conditions of 
distribution above quoted are much exceeded here, and 
hence the duty of our well waters would exceed the duty 
quoted (soil, average evaporation, and average humidity be- 
ing equal.) 



Year 


Pr. Apl & May 


Pr. June, July & Aug 


Total 


1882 


8.68 


13.18 


21.86 


1883 


6.59 


11.30 


17.89 


1884 


5.60 


9.47 


15.07 


1885 


6.26 


13.84 


20.10 


1886 


5.10 


9.12 


14.22 


1887 


5.11 


15.07 


20.18 


1888 


5.86 


7.67 


13.53 


1889 


6.45 


5.21 


11.66 


1890 


3.52 


8.01 


11.53 


1891 


3.89 


10.52 


14.41 


Avera 


ges 5.70 


10.34 


16.04 



TABLE NO. 14. 

Table of precipitation 
in Dakota during Apl. 
and May and during 
June, July and Aug. 
(From table No. 43.) 



45 

Then, too, the average Colorado precipitation of 18 or 19 
inches is less than the Dakota average of about 21 inches, 
so this operates still further to increase the probable duty 
of water here. 

In the recently published report of State Engineer J. P. 
Maxwell, of Colorado, (1890 report) are certain very perti- 
nent suggestions and estimates, relative to water duty 
which I cannot do better than to quote. 

"Water rights vested on the basis of the low duty assigned 
to water ten years ago, have, in instances , deteriorated lands 
and reduced their productiveness by as urfeit in application, 
while on adjoining lands through an enforced economy, a 
higher duty, better conditions of soil, and greater produc- 
tiveness have resulted." 

"Unskilled labor has a penalty of 25 to 50 per cent attach- 
ed to it in the application of water, and unfortunately this 
class is too prevalent in the irrigation fields, in many cases, 
no other being obtainable." 

"An abundant water supply tends to carlessness in its 
application and consequent waste. Where liberal and old 
water rights are provided, it is frequently the practice to 
turn the water upon the land and permit it to run without 
change or attention throughout the night ana sometimes 
during the day, a large volume of water soaking into the 
soil without benefit to the crop." 

"The duplication of ditches is another fruitful source of 
waste, reducing the duty of the volume of water." 

"Reference to some of the maps prepared by this depart- 
ment, will show, in different localities sev^eral ditches par- 
alleling each other at inconsiderable distances apart, the 
upper one of which could be made to answer the purposes 
of all with marked economy in water, as well as large sav- 
ing in capital." 

"Too little attention has been given to the proper prepara- 
tion of the surface to facilitate the rapid spreading of the 
water." 

"This is principally the result of too large individual own- 
ership of land, rendering it impracticable to give close sup- 
ervision and secure careful preparation of the land.'' 

"The best results will be obtained from small proprietary 
rights in land, and a consequent higher state of cultivation." 

The ownerships of the cultivated lands of the state 
should be multiplied by ten and the population increased to 
that extent." 

All that is here stated will apply with equal force to Da- 
kota, and he who would meet with the greatest measure of 
success will heed the cautions thus held out by so high an 
authority. 

Become an expert in irrigation by studying up from all 
available sources. Profit by the past experiences of others. 
Beware of attempting more than your means or experience 
will fully warrant and conserve well the supply of liquid 
wealth so freely granted you. 

The following table will serve to show the great range of 
duty in the same state, and as a very valuable basis of com- 



46 

parison with our own more favorable and less fluctuating 
climatic conditions. 

TABLE NO. 15. 

TABULATED STATEMENT OF WATER-DUTY ON STREAMS 
INDICATED FOR 1889 AND 1890. 







Bft 


a 


" 




C8 


5 






.^B-^ 




a^ 




S3 


a 


STREAMS GAUGED. 


discliarge 
20 to Sep 
20 in cubic 
second. 


-3 

■*^ 

> 




6X1 
.2 

1=1 -d 

cS C 


o 
> 

a 

o 









3 cS fH ^H 

S3 " O O 

oSj2 a 


fM 


> o 
to 


.2 S 
cc a 


"5 


p 






S 


< 


&3 


« 


E^ 


q 


Cache La Poudre . 


j 1889. 
■■■■( 1890. 


7.35.97 


139,222 


1.178 


0.682 


1.860 


189.168 


770.51 


139,222 


1.254 


0.338 


1..592 


180.687 


Big Thompson 


5 1889. 
•■•■ 1 1890. 


214.53 
425.42 


91.037 
89,790 


0.579 
1.192 


no data 
no data 




424.35 
211.06 


St. Vrain 


^ 1889. 


215.46 


94,013 


0.583 


0.532 


i.695 


436.33 


■■■■} 1890. 


284.238 


94.335 


0.739 






332.69 


South Boulder 


and] 1889. 

....I 1890. 

( 1889. 


461.97 

419.33 

60.40 


77,682 
76,682 
10,173 


1.406 

1.34 

1.46 






168.15 


Boulder Creek 






182.86 


Bear Creek 






168.42 


■■■■} 1890. 


33.98 


8,112 


1.03 






239.0-2 



From 1890 Report of State Engineer of Colorado. 

It will be noted that, in all the above cited estimates, the 
water is that of a natural stream the volume of which is 
largely augmented by seepage water. The water having 
been used at a higher level, seeps through the soil and finds 
its way back into the stream at a lower level, there to be 
used again and again, thus raising the duty, over a given 
area, of a given original volume. 

In the level lands of the Dakotas, and on the purely in- 
dividual system of irrigation which will prevail here, no 
account need be taken of seepage waters as a source of 
secondary supply; although the presence of seepage water, 
and the power of the soil to retain it, will go far towards 
determining the ultimate duty of the original well-supply. 

Quoting, again, from the Colorado report of 1888, Engineer 
Greene says, "it is thought that when distributed with the 
greatest care, and in suflScient quantities to be handled 
without great waste, during seasons of average rainfall and 
to crops and soils fairly conditioned to its economical use, 
that the duty of water should approach 90 acres to the sec- 
ond foot." 

Also "Two cubic feet of water per second carried on to a 
field in one body, will, under conditions otherwise the same, 
irrigate more than twice the area that one cubic foot carried 
alone would irrigate. 

What will be the conditions of the duty of w^ater under 
the Dakota well-system, and what the duty that may be 



47 

safely relied upon under average conditions? Note that 
the average rain-fall for 10 years has been 21.58 inches; the 
maximum 28.12 inches, and the minimum 14.68 inches. 

In this level country a rain-fall of 24 inches is sufficient to 
give abundant returns, and even less than that, with proper 
distribution and provided, the soil could be maintained, year 
after year, up to a proper standard of saturation. For the 
sake of conservatism, reduce the average annual rain-fall to 
18 inches, instead of 21 inches, then but 6 inches need be 
artificially supplied to give the maximum of 24 inches 
required ." 

Thus 6 inches may be taken to fairly represent the unit of 
duty required in Dakota. 

One cubic foot per second=448.83 gallons per minute. 
This amount is equaled, or exceeded, by most of the small- 
er wells of the state . 

One second-foot=: 10,368,000 cubic feet in 4 months, (which 
may be said to cover the irrigation season, from April to 
J uly) or a sufficient volume to cover 238 acres a foot deep, 
or 476 acres 6 inches deep. 476 acres may, therefore, be said 
to be the duty of a second-foot in that period of time. 

Allowing for deep seepage and evaporation, and call the 
actual duty 320 acres, instead of 476 acres (a loss of 156 
acres), and it would appear that a second foot is amply 
sufficient to serve a half section of land during a poor year. 

Account is not here taken of the fact that during the 
months prior to the beginning of the irrigation season, the 
land may be prepared, by flooding, to such an extent as to 
render further service during the irrigation season almost 
unnecessary; and the further fact, that, by a system of res- 
ervoirs, an enormous volume may be stored to supplement 
the supply of the well itself during the 4 months of irriga- 
tion service. Thus the supply of the well during eight 
months of the year may be utilized to swell the duty of 
the well during the 4 months of service, to the extent of 
making the duty during that period extend over fully 
double the area above assumed to represent the estimated 
duty. 

The difference in the uniformity of supply of the Colora- 
do rivers and the Dakota welis is most marked. The 1890 
gauging record of the Cache La Poudre river shows that the 
volume discharged during March varied from 50 to 150 
cubic feet per second. During April, from 75 to 500 cubic 
feet; increasing thence rapidly to June 2d, w^hen the dis- 
charge was 1825 cubic feet. The decrease was then quite 
rapid until the first of September, when it had fallen to less 
tban 100 cubic feet, and it so remained during the balance 
of the season .of discharge. The same is true of all other 
western rivers whose waters are derived from the melting 
snows of the- mountains. 



48 

There is therefore little chance to use the waters for pur- 
pose of irrigation except during the season of flood, or, in 
exceptional cases, where the waters are impounded in stor- 
age basins of great area. In Dakota, on the contrary, the 
supply is constant the year around. Winter and summer 
the flood pours forth with unabated energy, and the irrigat- 
or may — as he actually does — work in mid winter, with a 
hoe in his hand and a fur coat an his back. 

By reason of this periodicity the duty of the Colorado 
waters is limited to the actual duty during the irrigation 
season, and, contrariwise, the duty of the Dakota well 
should be measured by what might be fairly called its annu- 
al duty. 

I have little doubt but that the duty of the s( cond-foot 
in Dakota will be found, in the end, to be nearer 640 acres 
than 320 acres; but if, for the present, the lesser unite be 
adopted abundant alowance may be claimed and the claim 
be entitled to fair consideration by reason of its actual 
conservatism. 

From table No. 20, of second feet reduced to gallons per 
minute, the following table may be constructed on the 
basis of a duty of but 320 acres per second-foot. 

TABLE NO. 16. 
DUTY OF WATER IX DAKOTA. 

(New.) 



Gallons per 

minute from 

well. 


Equivalent 
in second ft. 


Duty in 
acres. 

320 

640 

960 

1280 j 
1600 


Gallons per 

minute from 

weU. 


Equivalent 
in second ft. 


Duty in 
acres. 


448 

897 
1346 
1795 
2244 


1 

2 
3 
4 


2692 
3141 

3590 
4039 

4488 


6 
7 
8 
9 
10 


1920 
2240 
2560 

2880 
3200 



49 

THE DIVISION AND MEASUREMENT OF 

WATER. 

It has bef n stated by Prof. L. G. Carpenter, in his work 
on the above subject, that "one of the most important, as 
well as one of the most difficult problems of irrigation is 
that of making a just distribution of water." Keference 
being made to the distribution of irrigation waters in Col- 
orado and elsewhere where irrigation is carried on on a vast 
scale and by means of waters taken from large ditches or 
canals which serve a large area and are supplied from rivers 
or great storage reservoirs in the mountains. 

Every device which the ingenuity of the centuries could 
devise has been used to render this division more equitable, 
certain and economical and to prevent waste where, as is 
usually the case, the economy of water is of the first im- 
portance. 

The literature of the subject is voluminous, but the Da- 
kota farmer will look far, and in vain, for any information 
touching upon conditions similar to his own." 

We have here no vast system of canals, nor will we have 
in the future; no vast storage basins and no need of the 
many devices used in other sections for the division and 
measurements of water. Our system is essentially individ- 
ual, but the day is at hand when certain simple devices will 
be required to divide the waters of our wells among the few 
consumers under service by each well operating under the 
township well law, or among those who rent water from the 
individual owners of a well. 

With us, too, it is not wholly a matter of device for the 
mere measurement of a given volume, or a question as to 
the unit of volume; but very largely a matter of legislation 
based upon our peculiar conditions and needs, which legis- 
lation has yet to be evolved and put to the test of practice. 

Contract, too, will enter largely into the matter of the 
division of water and, on the start, the terms will be more 
varied and uncertain than the devices necessary to carry 
them out. With the Dakota farmer, as with farmers else- 
where, the central idea will be to secure the greatest possi- 
ble service from the water at hand; and the prevention of 
waste will soon demand attention. 

In the irrigation operations of the west all the elements 
are predetermined. The water supply is known, the ditches 
or canals are constructed of a certain size to perform a cer- 
tain service or serve a given area. This service cannot well 
be exceeded and great economy must be observed in order 
that the actual service may equal the calculated service. 
Here— the main chanel or source of supply is the well, the 
volume of which is easily determined. The fountain head 
may be inexhaustible but only so much can be drawn off. 
The farmer may have a surplus which he may waste or 



50 

sell to his neighbor, in which case economy in his own use 
and in theirs will operate to increase his revenue from the 
sale of the surplus. 

So, too, in the operation of the township wells. The great- 
est service will be desired for each consumer and the well 
will be called upon to serve as many consumers as possible. 
In the latter case, as in the case of an individual owner, 
proper service to each consumer can only be had through 
the medium of a storage reservoir; for if a well will not — 
on the instant— serve one consumer fully it will certainly 
fail to serve several consumers. 

EACH MUST HAVE HIS OWN RESERVOIR. 

Herein will arise questions as to the manner of service, 
priority, etc. 

Suppose a well serves four quarter sections (say the E. 3^ 
of Sec. 1 and the E. % of Sec. 12) and that by reason of the 
slope of the ground it is necessary to locate the well on the 
center of the iST. E. M of section 1. If the water is carried 
in a ditch to the other quarters, and the amount delivered 
is measured at the well, the owner of the S. E. 34 of Sec. 12 
would receive far less water than the owner of the X. E. 34 
of Sec. 1 because of the far greater loss by evaporation and 
seepage. His loss, too, would be his neighbor's gain. 

If the water be distributed in a pipe line the loss of head 
due to friction in the longer pipe would operate to the same 
end but to a lesser extent. 

Again — if each consumer measures his water at the point 
of delivery in his own reservoir a question will arise as to 
the priority of service. A may fill his reservoir first and D 
last, but meanwhile the water in A's reservoir has been low- 
ered a foot or two by evaparation and seepage and, at the 
period when greatest service is required, A may receive 20 
per cent less service than D, yet each has received and paid 
for the same volume of water. If the service to the several 
reservoirs is by pipe line and is simultaneous the inequali- 
ties will be less and more easily subject to regulation. 

It is not the intention here to raise any question as to the 
details of distribution or the possibility of an equitable 
division of the water; nor the purpose to suggest remedies 
for anticipated controversies, but it must be known that 
questions of detail, such as those above suggested, will arise 
and demand a solution. When they do a solution will be 
found on lines of equity to all interests. 

Notwithstanding our conditions are so wholly different 
from those met elsewhere, the measurement of the volume 
of our wells must be treated the same, hov/ever much the 
final divisions of the waters may differ. 

Heretofore too little attention has been paid to the accu- 
rate determination of the volumes of our wells. Usually 
the volume has been guessed at or an approximate estimate 
has been made by timing the filling of a barrel, hogshead or 



tank. In some cases the stream has been weired and an ac- 
curate estimate made as to the volume. 

In a few cases grossly exagerated reports have been cir- 
culated as to the volume of certain wells (notably the Risdon 
wfll at Huron, which has been advertised as having a vol- 
ume of 10.000 gallons per minute, whereas its true volume 
is but 2,250 gallons per minute.) 

Such exagerations can only result in harm and should be 
discouraged. The truth is sufficiently ivoiiderfid to satisfy 
the most exacting. 

UNITS OF MEASUREMENT. 

THE STATUTE INCH, is a unit of water measurement 
much used in the western states and territories. It varies 
in different states and even in different sections of the same 
state. It is equal to about 45 cubic inches per second. One 
second foot=38.4 statute inches in Colorado. This unit is 
practically the same as the miner's inch it being the miner's 
inch in the terms of a specific statutory specification. It 
varies in different states. 

THE MINER'S INCH Is fully explained and illustrated 
in tables 18 and 19 and the accompanying notes and figures. 
When defined by state law it is known as the statute inch. 

THE ACRE FOOT is equal to 43,560 cubic feet or such an 
amount as will cover one acre to a depth of one foot (See 
table 21 and notes & P. 60). This unit is more largely one 
of service than of measurement. 

THE SECOND EOOT, or cubic foot per second, (See 
table 20 and note following.) is a unit definite as to both 
volume and time and is the one upon which all wier tables 
are constructed and is no doubt the coming unit in this 
and other countries. 

GALLONS PER MINUTE. Like the second foot this 
unit is definite as to both volume and time and is the one 
commonly used in Dakota. (See tables, 19 20, 36 and 37.) 

Two general methods have been adopted in the division 
and measurement of water. 

THE FIRST is known as the DIVISOR, the object of 
which is to divide the waters of the ditches or streams into 
certain proportionate parts among consumers. The idea is 
not to measure according to some fixed unit but simply to 
divide or proportion the water according to a certain ratio. 
3^ to each of two consumers; % to each of three, &c &c 

THE SECOND is known as the MODULE the purpose of 
which is not to divide but to measure according to some 
fixed unit. In Spain, Italy and India measuring devices or 
modules have been in use for centuries but of late years 
they have reached their greatest perfection in our western 
states 

Of all measuring devices the WEIR has proved to be the 
most acurate and satisfactory. (See the following table of 
weir measurements, table 17) 

The rectangular weir wherein the crest is horizontal and 
the sides vertical is the common form and the one to which 



52 

the tables herein given apply. The trapezoidal weir has the 
crest horizontal and the sides sloping; this form possesses 
certain advantages which will not, however, be considered 
here. The triangular weir or notch is likewise claimed to 
possess certain advantages over other forms. 
THE SPILL BOX. 

Among the most satisfactory devices for the division and 
measurement of water is the excess weir or spill-box, invent- 
ed by Mr. A. D . Eoote of Idaho and illustrated in Fig. 6, 
wherein A is the main ditch the tlow in which may be check- 
ed by gate B thus forcing a portion of the water into the 
spill-box D which has an opening F in the side, the discharge 
through which into the lateral ditch G is regulated by a 
slide and graduated scale as shown. The inner edge E E of 
the box is lower than the ends and outer side so that all 
water not passing through the opening F spills back into 
the main ditch. The head or height of the water above the 
opening being regulated by the height of the edge E E. 

By this means the head at the opening F is maintained 
constant at all stages of the water in the main ditch and the 
amoun of water discharged through an opening of any 
length is not subject to fluctuations due to change of head 
but remains constant. ISTot over a foot of fall need be lost 
to the main ditch by using this device. The spill edge E E 
should be beveled to give a sharp edge, on the box side, over 
which the water may flow without friction. This form of 
module will flnd a wide field of usefulness in Dakota as the 
practice of irrigotion becomes more general and its details 
more closelv considered. 




spHl'Box. 



Fig. 6. SpiU Box. 

THE EECTANGULAR WEIR. 

This form of module or measuring device having been the 
subject of the most exhaustive investigation, is consdered 
to be the best suited to the accurate measurement of water. 

The conditions of its proper operations are : 
1st. That the crest shall be horizontal and the sides vertical. 
2d. That the up-stream face be vertical. 
3d. That both the crest and sides be sharp edges on the up-stream side . 



■a- 



4th. That the depth of water flowing? over the weir be not less than 3 nor 
more than 25 inches. 

That the depth of water flowing over the crest be not greater than 
^3 the length of the weir. 

That the weir opening be not over % the width of the stream ap- 
proaching it. 

That the discharge over the weir should be free and the approach of 
the water without velocity sufficient to produce eddies. 
That the distance from the crest to the bottom of the channel— and 
from the ends of the weir to the sides of the channel, shall be at least 
twice as great as the depth of the water flowing over the weir. This is 
to secure complete contraction. 

Weirs may have either partial or complete contraction as 
illustrated by figures 1 to 5 of Fig. 7. 



5th. 
6th. 
7th. 
8th. 




Illustrating Contraction on Weirs. 



In following over a weir water takes the form shown in Fig 
1. The upward movement of the water toward the crest A 
of the weir A B causing the water to arch upward as shown. 
The true head, as shown at c, is reduced by the downward 
curve of the water, as shown at d e. This is called the con- 
traction. If the weir has the form shown in Fig. 2 the con- 
traction of the flow will be but partial; that is, there will 
be contraction at the crest a c but none at the sides a b 
and c d past which the water flo^\'S as shown in Fig. 4. 
If the weir has the form shown in Fig. 3 the contraction is 
said to be complete, for, in addition to the contraction at 
the crest, there is also contraction at each side, a b and 

where it is seen that the width of 
a is less than the width of the 
illustrate not only the action of 
meaning of the term ''Complete 
Contraction." which is a requisite to the proper application 
of the following table of weir measurements. 
TO CONSTRUCT A WEIR AND MEASURE THE VOL- 
UME OF A WELL. 
Select some convenient point where, by throwing up a 
low bank, a small pond may be formed by the stream from 
the well. Across the outlet set a board or plank out of 
which has been cut a rectangular piece (say 12 inches deep 
by 4 feet long). Support the board by nailing to stakes 
driven into the ground taking care that the edge of the 



c d, as shown in Fig. 5 
the outflowing stream 
opening b. This will 
flowing water but the 



opening is level or horizontal. Make the bank water-tight 
about the bottom and ends of the weir. Drive a stake sev- 
eral feet back of the weir and near the edge of the pond 
making the top of the stake level with the crest of the weir 
either by using a level < r by driving the stake to water 
level at the moment the water begins to spill over the weir. 








to — 

CO © 

Sec 

^1 



a, S 

O . 

S o 

"^ ft 



St( 



9 CO 

■^3 o 

I J 

S a 

B § 

. "^ 

bf re 






00 

Permit the water to rise to the full height at which it will 
stand while flowing over the weir. Then measure the depth 
of water over the stake. 

Enter the weir table with this depth (as explained in ex- 
amples given) and get the quantity -for one inch. Multiply 
this quantity by the length of the weir in inches to get the 
total volume flowing from the well, in cubic feet per minute. 

If possible have the up-stream edges of the weir lined 
with strips of tin or sheet iron to give a sharp edge for the 
water to flow over. If this is not at hand then bevel the 
crest and sides of the weir to a sharp edge on the up-stream 
side. See, in short, that ALL the conditions mentioned on 
page 53 have been complied with. The manner of con- 
structing and using a weir is illustrated on the opposite 
page, where A is the weir board with the beveled notch or 
opening B. E is the stake driven back to the side of the 
weir, out of the current, and from which the true depth is 
taken as shown. 

Application of Weir Table ^o. 17. 

This table gives the number of cubic feet of water passing 
per minute over eaoh inch in width of a weir, and tor depths 
from iV inch to 25 inches. 

The top horizontal line of fractions are the fractions of an 
inch in depth, and the columns of figures at the rigr.t 
and left ends indicate the full inches of depth. The quan- 
tities inside the table are the cubic feet discharged. 

Thus 7s inch of depth= .11 cu. ft. per inch width of weir, f See at ^ 
10 inches " " =12.71 " . " " " " '•'***** ! 
lOJi " " " =13.19 " 'c » » " " i in the [ 

16ii " " " =27.43 " " " " " " L table J 

These examples will render clear the use of the table 

Examples of Use. How many cubic feet and gallons are 
discharged per minute by a well the water of which, in flow- 
ing over a weir 5 feet long, shows a depth of 1% inches? 

I'rom table the quantity of water for one inch wide by 7% 
inches deep=8.05 cubic feet per minute: 5 feet wide=60 
inches; therefore 8.05 multiplied by 60=483 cubic feet per 
minute. Referring to table No, 36 we find that 488 cubic 
feet=3612.8 gallons. Therefore by this simple process the 
volume of our well per minute has been" found to be 483 cu- 
bic feet, or 3612.8 gallons per minute. 

The work involved in the construction of a weir is but 
slight, and the calculation of the flow, as above, is a mere 
matter of multiplication and addition. Every well owner 
should see that the volume of his well is accurately deter- 
mined in this way; and not once alone, but every few 
months, in order to know whether there is any increase or 
diminution in the flow . A series of such systematic tests 
would no doubt result in furnishing valuable information 
leading up to a correct determination as to the source and 
supply of the artesian stream. 



56 



TABLE NO. 17. 

"WIEPw MEASUREMENTS. 



'Z 

fc 


■s. 


- 


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57 

Certain refinements of calculation enter into the matter 
of measurement by weirs, but they have not sufficient bear- 
ing on the ordinary practice to deserve more than mention 
here. Tables of weir measurements are constructed where- 
in these elements have been taken into account, but the 
table given is sufficiently accurate for our use. In view of 
the fact that the table given may not meet all the require- 
ments of practice the formula upon which the most accurate 
weir measurements are based is here given and briefly 
explained. The weir formula of Francis is as follows: 

Y=C (L— .2 H) Hf 
Wherein V=Tolume in cu ft per sec. flowing over the weir 

C=The coefficient of discharge (=3.33) (or 3.3333^-) 

L=The length of the weir in feet. 

H=The head, or depth of water over the weir.. 

t=The square root of the cube of H. 

Substituting the value of C, the formula becomes, 
V=3.33 (L— .2H)Hf 

Which reads as follows: 

Volume per second=3.33 multiplied hy (the length of the 
weir less two tenths of the head) multiplied by the square 
root of the cnihe of the head. 

This will be rendered plain .by an illustration. 

What will be the discharge per second over a weir 10 feet 
long if the water is 1.5 feet deep ? 

The total length L of the weir is reduced, by reason of the 
contractions at the ends, to the calculated amount of yV of 
the depth, or head, for eacJi contraction, hence the expres- 
sion (L— .2H) 

In the example the depth=1.5 feet, ^^ ot which (there 
being 2 contractions) is= .3, and ten feet— the full length- 
less .3=9.7 feet, or the elective length. 

The cube of 1.5 (the head) =3.375 and the square root of 
3.375=1.837. We now have the formula thus: 
V=3.33X9.7X 1.837. 

Which multiplied through=59.39 cubic feet per second 
flowing over the weir. 

The cubes and roots in these calculations may be taken 
directly from the tables given elsewhere herein. This 
amount is somewhat less than that resulting from the use of 
the weir table, but the table is sufficiently accurate for all 
practical uses. The use of the formula may, in some eases, 
be more convenient and hence it has been given . Ordinar- 
ily the formula is given thus. 

V=3.33 L Hf 
no account being taken of the loss to L resulting from the 
end contractions. If a weir is used wherein there are no end 
contractions then this last form of formula would be used. 
If the opening is obstructed by a central post there would 
be 4 contractions and the expression of the formula would 
be (L— .4H), and so on for any other number of contractions. 



58 



TABLE NO. 18. 

TABLE OF miner's INCHES 

Reduced to Cubic Feet and Gallons and to Cub. Ft. and Gals, per Minute. 
(Corresponding with the " Colorado " inch.) New. 



Miner's 


Equivalent in 


Equiv. in cu. 


Equivalent in 


Equiv. in Gals. 


Inches. 


Cubic Feet. 


ft. per minute. 


Gallons. 


per minute. 


1 


.0259337 


1.556024 


.194 


11.64 


2 


.0518674 


3.112048 


.388 


23.28 


3 


.0778011 


4.668072 


.582 


34.92 


4 


.1037348 


6.224096 


.776 


46.56 


5 


.1296685 


7.780120 


.970 


58.20 


6 


.1556022 


9.336144 


1.164 


69.84 


7 


.1815359 


10.892168 


1.358 


81.48 


8 


.2074696 


12.448192 


1.552 


93.12 


9 


.2334033 


14.004216 


1.746 


104.76 


10 


.2593370 


15.560240 


1.940 


116.40 


20 


* .52 


* 31.12 


* 3.88 


* 232.8 


30 


.78 


46.68 


5.82 


349.2 


40 


1.04 


62.24 


7.76 


465.6 


50 


1.30 


77.80 


9.70 


582.0 


60 


1.56 


93.36 


11.64 


698.4 


70 


1.82 


108.92 


13.58 


814.8 


80 


2.07 


124.48 


15.52 


931.2 


90 


2.33 


140.04 


17.46 


1047.6 


100 


25.93 


155.60 


19.40 


1164.0 


200 


51.87 


311.20 


* 38.8 


2328. 


300 


77.80 


466.80 


58.2 


3492. 


400 


103.73 


622.40 


77.6 


4656. 


500 


129.67 


778.01 


97.0 


5820. 


600 


155.60 


933.61 


116.4 


6984. 


700 


181.54 


1089.21 


135.8 


8148. 


800 


207.47 


1244.81 


155.2 


9312. 


900 


233.40 


1400.42 


174.6 


10476. 


1000 


259.34 


1556.02 


194.0 


11640. 


10000 


2593.37 


15560.24 


1940.0 


116400. 



* Note the change in location of the decimal point at * * * * * 



Fig. 9. 
Miner's Inch Measurement. 




The Miner's Inch is such a quan- 
tity of water as will flow through 
an aperture one inch square in a 
board two inches thick, under a 
head of water of 6 inches, in one 
second of time and it is equal to 
0.194 gallon, or 11.64 gallons per 
minute; and to .0259337 cubic foot, 
or 1.556024 cubic feet per minute. 
Fig. 9 shows a trough with 6 inches 
depth of water in it, and with a 
through which is cut a hole 1 inch 



2 inches thick 
If the depth of water is maintained at 6 inches one 
inch per second would be discharged through the 



bottom 
square, 
miner's 
hole. 

This unit of water measurement has been and is very extensively used 
in the west in mining operations, irrigation and the guaging of streams 
and ditches but it is largely giving way to more definite units. By reason 
of the difference in the head of water over the opening, the value of the 
miner's inch varies in different states from 1.36 to 1.173 cubic feet per min- 
ute. The head varies from 3 to 10 inches and in some cases it is measured 
from the top of the opening, (in the side of the box or flume) in other 
cases from the bottom and in still other cases— and properly— from the cen- 
ter of the opening. 



59 



Then, too, the volume discharged under a given head, and 
from a given area of opening, varies as the form of the 
opening is changed— thus, 36 miner's inches will be discharg- 
ed through an opening one inch high by 36 inches long, and 
also from an opening 6 inches high by 6 inches wide, (the 
area of the opening being the same) yet, as a fact, more 

water will flow through the latter opening because it flows with less re- 
sistance from the edges of the opening. In the first case the edges of the 
opening measure 74 inches, while in the second case they measure but 24 in. 
The volume discharged is further varied by the form of the edge, i. e., 
whether it be square, rounded, sharp or beveled ; and further still by the 
thickness of the edge — whether it be one inch or more. It being manifest- 
ly impossible, over any extended area, to secure any uniformity in the head 
of water maintained, or in the form or thickness of the edges of the outlet, 

oi in the ratio of the area 
of opening to wet perime- 
ter, it is impossible to 
maintain any standard of 
value for the miner's inch 
except within the limits 
stated. The Colorado inch 
most nearly corresponds 
with the theoretical dis- 
charge. The California 
inch, as usually measured, 
is from an aperature 2 
and inches high of any 
desired length, though a 
plank 1^4 inches thick as 
shown in Fig. 10. The bot- 
tom of the aperature being 




Miner's Inch Measurements. 



Fig. 10. 

2 inches above the bottom of the flume. This secures a complete contract 
tion of the stream. The value of the inch will increase as the orifice is 
enlarged, as shown in the following table. 

TABLE NO. 19. 

TABLE OF MINER'S INCH MEASUREMENTS. 
From Pel ton Water Wheel Co. 



Length 


Opening 2 inches 


high. 


Opening 4 inches high. 


of 


Head to 


Head to 


Head to 


Head to 


Head to 


Head to 


openi'g 


center 5 


center 6 


center 7 


center 5 


center 6 


center 7 


in 


inches. 


inches. 


inches. 


inches. 


inches. 


inches. 


inches . 


Cubic ft. 


Cubic ft. 


Cubic ft. 


Cubic ft. 


Cubic ft. 


Clubic ft. 


4 


1.348 


1.473 


1.589 


1.320 


1.4.50 


1.570 


6 


1.35.5 


1.480 . 


1.596 


1.336 


1.470 


1.595 


8 


1.359 


1.484 


1.600 


1.344 


1.481 


1.608 


10 


1.361 


1.485 


1.602 


1.349 


1.487 


1.615 


12 


1.363 


1.487 


1.604 


1.352 


1.491 


1.620 


14 


1.364 


1.488 


1.604 


1.354 


1.494 


1.623 


16 


1.365 


1.489 


1.605 


1.356 


1.496 


1.626 


18 


1.365 


1.489 


1.606 


1.357 


1.498 


1.628 


20 


1.365 


1.490 


1.606 


1.359 


1.499 


1.630 


22 


1.366 


1.490 


1.607 


1.359 


1.500 


1.631 


24 


1.366 


1.490 


1.607 


1.360 


1.501 


1.632 


26 


1.366 


1.490 


1.607 


1.361 


1.502 


1.633 


28 


1.367 


1.491 


1.607 


1.361 


1.503 


1.634 


:% 


1.367 


1.491 


1.608 


1.362 


1.503 


1.635 


40 


1.367 


1.492 


1.608 


l.,363 


1..505 


1.637 


50 


1.368 


1.493 


1.609 


1.364 


1..507 


1.639 


60 


1..368 


1.493 


1.609 


1.365 


1.508 


1.640 



This table shows the discharge in cubic feet of each miners' inch of the 
openings given in the table. For an opening 2 inches high by 20 inches 
long and 5 inch lead the total discharge per minute would be 1.365X40=54.6 
cubic feet. (2 inches by 20 inches=40 inches=area of opening.) 



60 

The following brief table, by C. L Stevenson, C. E., of 
Salt Lake City, shows at a glance the relationship between 
the different units of water measurement with sufficient 
accuracy for ordinary calculation. It will be valuable for 
ready reference. 

1 cu. ft. per second equals: 



2 acre feet in 24 hours. 
60 acre feet in 30 days. 
180 acre feet in 3 months. 
730 acre feet in 1 year. 



7 .5 gallons per second. 
449 gallons per minute. 
50 California inches, 
38.4 Colorado inches. 



100 California inches equal 



4 acre feet in 24 hours 
1 acre foot in 6 hours. 
120 acre feet in 30 days. 
360 acre feet in 3 months. 
1460 acre feet in 1 year. 

100 Colorado inches equal: 



15 gallons per second. 
900 gallons per minute. 
77 Colorado inches. 
2 cubic feet per second. 



19.5 gallons per second. 
1,170 gallons per minute. 
2.6 cubic feet per second. 
130 California inches. 



5^ acre feet in 1 hour. 
1 acre foot in 4.2 hours. 
155 acre feet in 1 month. 
465 acre feet in 3 months. 
1,886 acre feet in 1 year. 

The unit of the miner's inch wiU find no place in Dakota. Mention has 
been made of it here because it is so extensively used elsewhere and is so 
frequently referred to in the irrigation literature of the day. 

TABLE NO. 20. NOTE. 



"SECOND FEET" 

REDUCED TO GALLON S. 

New. 



No. of 


Equivalent 


Equivalent 


second 


in gallons 


in gallons 


feet. 


per second. 


per min'te. 


M 


1.87 


112.2 


^2 


3.74 


224.4 


% 


5.61 


336.6 


1 


7.48 


448.8 


2 


14.96 


897.6 


3 


22.44 


1346.4 


4 


29.92 


1795.2 


5 


37.40 


2244.0 


6 


44.83 


2692.8 


7 


52.36 


3141.6 


8 


59.84 


3590.4 


9 


67.32 


4039.2 


10 


74.80 


4488. 


20 


149.61 


8976. 


30 


224.41 


13464. 


40 


299.22 


17952. 


50 


374.02 


22440. 


60 


448.83 


26928. 


70 


523.63 


31416. 


80 


598.44 


35904. 


90 


673.24 


40392. 


100 


748.05 


44883. 


200 


1496.1 


89766. 


300 


2244.2 


134649. 


400 


2992.2 


179532. 


500 


3740.2 


224412. 


1000 


4780.5 


448330. 



The unit of water measurement 
known as the SECOND FOOT is very 
largely used in the west where it is be- 
coming more popular because it is a 
unit whose value cannot be disputed. 
A second foot is one cubic foot per 
second. This is definite as to a deter- 
minable volume discharged within a 
determinable time, and thus is estab- 
lished a unit most capable of expres- 
sion in the terms of ordinary calcula- 
tions. 

It might be well if such a unit were 
used to express the volume of our 
wells but the unit of gallons-per-min- 
ute has, by usage, become established 
and it will probably be retained. 
Some equity, too, may be urged in the 
retention of the gallon unit, as applied 
to wells, instead of the adoption of 
the larger unit of the second foot yA\\c\\. 
is more applicable to the greater vol- 
umes to which it is applied in the 
greater irrigation operations of the far 
west. 



61 
TABLE NO. 21. 

VOLUME AND WEIGHT OF WATER ON ONE ACRE. 



Xeti: 









Weight, at 62. 


425 pounds to the 


Depth in 


Cubic feet of 


Grallons. 


cubic foot. 


inches . 


water. 














Tons and Pounds. 


1 


36.30 


27153 


113 


603 


2 


7260 


54308 


226 


1206 


3 


10890 


81462 


339 


1809 


4 


14520 


108616 


453 


411 


3 


18150 


135771 


566 


1014 


6 


21780 


162924 


679 


1618 


7 


25410 


190079 


793 


220 


8 


29040 


217234 


906 


822 


9 


32670 


244388 


1019 


1424 


10 


.36300 


271542 


ll:« 


•27 


11 


399:30 


298695 


1246 


630 


12 


43560 


325850 


1359 


12:33 



Xote: For amounts less than 1 inch cut off one place to 
the right for tenths and two places for hundredths, thus — 
For .1 inch Cu. ft. = 363.0 and Gals. = 2715.3. 
" .01 " " = 36.3 '' " = '^71.53 



Example: Required the volume for fall of 7.88 inches? 



7. inches 
.3 " 

.08 " 



7.38 



= 25410 cu. ft. 190,079 gallons. 

= 1089 " 8,146.2 

= 290.4 '' 2,172.34 " 



= 26,789.4 



200,397.54 



1 ACRE FOOT = 43,560 cubic feet, or sufficient water to 
cover the acre to a depth of one foot. 

This unit is the most recent of the units of water measure- 
ment. The element of time is entirely eliminated and the 
element of volume is specifically fixed in the terms of the 
definite unit, the cubic foot. 

The unit is largely used in representing the capacity of 
storage reservoirs, since it conveys a definite or comprehen- 
sible idea as to the service of the water stored. To say that 
a reservoir will hold 4,356,000 cubic feet conveys but little 
knowledge to the average man; but to say that the reservoir 
will hold 100 acre feet of water conveys at once the idea as 
to the service which will be rendered by the impounded wa- 
ter. The unit is, therefore, what may be properly termed a 
SERVICE iTNiT, and it fully answers this purpose. 

The last column of Section A, of Table No. 34, will give 
the cubic feet in the number of acre-feet represented by the 
acres of the first column, and Section B the corresponding 
number of gallons, while Section C will show the time re- 
quired for wells of different volumes to throw this amount 
of water. 



62 
TABLE NO. 22. 
From Trautwine's "Civil Engineer's Pocket Book.'' 



HYDRAULICS. 



TABIiE 2. Weight of W^ater (at 62^ lbs. per cubic foot) 
contained in one foot length of pipes of different bores. 

(Original.) 



Bore. 


Water. 


Bore. 


Water. 


Bore. 


Water. 


Bore. 


Water. 


Ins. 


Lbs. 


Ins. 


Lbs. 


Ins. 


Lbs. 


Ins. 


Lbs. 


Vs 


0.005305 


4 


5.43234 


14>^ 


71.3843 


40 


543.234 


H 


0.021220 


4^ 


6.13260 


15 


76..3922 


42 


598.915 




0.047745 


4^ 


6.87530 


15}^ 


81.5699 


44 


657.318 


0.084880 


7.66044 


16 


86.9174 


46 


718.427 


0.132625 


5 


8.48803 


16>^ 


92,4346 


48 


782.257 


3^ 


0.190981 


5^ 


9.35805 


17 


98.1216 


50 


848.803 


Vh 


0.259946 


53^ 
5% 


10.27051 


173^ 


103.9783 


52 


918.065 


1 


0.339521 


11.22542 


18 


110.0048 


54 


990.044 


1^ 
IK 


0.429706 


6 


12.22276 


183^ 


116.2011 


56 


1064.738 


0.530502 


6^ 


13.26254 


19 


122.5671 


58 


1142.149 


0.641907 


63^ 
6% 


14.34477 


193^ 


129.1029 


60 


1222.276 


1^ 


0.763922 


15.46943 


20 


135.8084 


62 


1305.119 


m 
m 


0.896548 


7 


16.63653 


21 


149.7288 


64 


1390.678 


1.0.39783 


^% 


17.84608 


22 


164.3282 


66 


■ 1478.954 


1% 


1.193629 


73^ 


19.09806 


23 


179.6067 


68 


1569.946 


2 


1.358084 


7M 


20.39249 


24 


195.5642 


70 


1663.653 


2ii 
251 


1.533150 


8 


21.72935 


25 


212.2007 


72 


1760.077 


1.718826 


834 


23.10865 


26 


229.5163 


74 


1859.218 


1.915111 


8^ 


24.53040 


27 


247.5109 


76 


1961.074 


23^ 


2.122007 


8^ 


25.99458 


28 


266.1845 


78 


2065.646 


2% 


2.339512 


9 


27.50121 


29 


285.5372 


80 


2172.935 


2jt 


2.567628 


9^ 


30.64178 


30 


305.5690 


82 


2282.940 


2.806354 


10 


33.95211 


31 


326.2798 


84 


2395.661 


3 


3.055690 


103^ 


37.43220 


32 


347.6696 


86 


2511.098 


3^ 


3.315636 


11 


41.08205 


33 


369.7385 


88 


2629.251 


3.586191 


113^ 


44.90166 


34 


392.4864 


90 


2750.121 


3% 


3.867.357 


12 


48.89104 


35 


415.9133 


92 


2873.707 


33^ 

3% 


4.159133 


12^/^ 


53.05017 


36 


440.0193 


94 


3000.008 


4.461519 


13 


57.37906 


37 


464.8044 


96 


3129.026 


3% 

3j| 


4.774515 


133^ 


61.87772 


38 


490.2685 


98 


3260.761 


5.098121 


14 


66.54613 


39 


516.4116 


100 


3395.211 



The w^eight of water in a given length (as one foot) of any pipe or other 
circular cylinder is in proportion to the square of the bore, or 

inner diameter. Hence the weight of water in 1 foot length of any cylinder of 
other diameter tha;n those in the table can be found by multiplying that for a 1 
inch pipe, 0.339521, by the square of the inner diameter of the given cylinder in 
inches. Thus, for a cylinder 120 inches diameter: diameter 2 = 120^ = 14400, 
and weight of water in 1 foot depth = 0.339521 X 14400 == 4889.10 lbs. Similarly, 
(t%)^ = aVe = 0-191406, and 0.339521 X 0.191406 = 0.064986 lb. = weight in 1 foot 
of y'^g inch pipe. Here, also, j"g= half of ^; hence, weight for y^ inch = one- 
foarlh of weight for | inch = one-fourth of 0.259946 = 0.064986. 

Weight of one square inch of crater 1 foot high, at 62^ lbs. per 
cubic foot = 62.25 -v- 144 = 0.432292 lb. 

For further information respecting weight of water, see page e 61 & €8 



63 



TABLE NO. 23. 

TABLE OF WEIGHT OF WATER. 

Maximun density is at 39.8° Fahr. 



Nevj. 



Cubic feet. - 


= 


Pounds . 


Gallons. = 


= 


Pounds . 


1 




62.425 


1 




8. 3216 


2 




124.850 


2 




16.6432 


3 




187.275 


3 




24.9648 


4 




249.700 


4 




33.2864 


5 




312.125 


5 




41.6080 


6 


* 


374.550 


6 


V! 


49.9296 


7 


* 


436.975 


7 


«• 


58.2512 


8 


* 


499.400 


8 


•K- 


66.5728 


9 




561.825 


9 


^J 


74.8944 


10 


.1^ 


624.250 


10 


C8 


83.2160 


20 





* 1248.50 


20 


"S 


* 166.432 


30 


'o 
p. 


1872.75 


30 


'3 


249.648 


40 


2497.00 


4« 


A 


3:52.864 


50 




3121.25 


50 


% 


416.080 


60 


3745.50 


60 


s 


499.296 


70 


s 


4369.75 


70 


'S 


582.512 


80 


TS 


4994.00 


80 


® 


665.728 


90 


=M 


5618.25 


90 


:«-i 


748.944 


100 


o 


6242.50 


100 


o 


832.160 


200 


o 


* 12485.0 


200 


el 


* 1664.32 


300 


'+i 


18727.5 


300 




2496.48 


400 




24970.0 


400 


03 


3328.64 


500 


o^ 


31212.5 


500 




4160.80 


600 


^ 


37455.0 


600 




4992.96 


700 




43697.5 


700 


a 


5825.12 


800 


61! 


49940.0 


800 


© 
a 


6657.28 


900 


g 


56182.5 


900 


7489.44 


1000 


c6 


62425.0 


1000 


<A 


9321.60 


2000 


t> 


* 124850. 


2000 


'S 


* 16643.2 


3000 


© 


187 275. 


3000 


© 


24964.8 


4000 


249 700. 


4000 


■B 


33 286.4 


5000 




312 125. 


5000 


© 


41608.0 


6000 


c 


374 550. 


6000 


o 


49929.6 


7000 


z 


436975. 


7 000 


z 


58 251.2 


8000 




499400. 


8000 




66 572.8 


9000 




561825. 


1 9000 




74894.4 


10 000 




624250. 


1 10 000 




83216.0 


100 000 




6 242 500. 


i 100 000 




832 160.0 


1000 000 




62 425 000. 


' 1000000 




8 321 600.0 



For ordinary purposes the weight of a cubic foot of water may be taken 
to be 62^^ pounds. The weight varies with the temperature as shown in 
the following table. 



Temperature 
Fahrenheit. 



Lbs. per 
cubic ft. 



Temperature 
Fahrenheit. 



Lbs. per 
cubic ft. 



32" 
40° 
50° 
60° 



freezing . 



.62.417 I 70° 62.302 



.62.423 
.62.409 
.62.367 



80° 62.218 

90° 62.119 

212° boiling 59.675 



Cubic foot of ice = 57.2 lbs. 

Cubic foot salt or sea water = 64.31 lbs. 

35.84 cubic feet of water weighs one ton. 

39.13 " " ice " " " 

2.311 feet of water = 1 lb. per square inch. 

1 cubic inch of water = .036024 lb. approximately. 

1 " " '• = .576:384 ounce. 

1 U. S. Pint = 1.0402 lb. of water. 

1 U. S. Quart = 2.0804 lb. of water. 

1 U. S. GaUon = 8.3216 lb. of water, {m) 

1 U. S. Wine barrel-31i/2 Gal. = 262.131 lb. of water. 

Tratctwine and Haswell, 



TABLE NO. 24. 
PRESSURE OF WATER. 

TSe pressure of water in pounds per square inch for every foot in height to 
300 feet; and then by intervals, to 1000 feet head. By this table, from the pounds 
pressure per square inch, the feet head is readily obtained; and vice versa. 



VM 


FrM!itttc 


U ^i 


Prenure 


.Feet 


Preemre 


1 Feet 


Preuure 


-Feet 


Presaure 


9mA. 


"-or" 


OfA. 


per aqiikre 
incti. 


Head. 


per square 
ineb. 


Head. 


per gquare 
incb. 


Bead. 


persquare 
iDcli. 


1 


S:S 


■6S 


28.15 


129 


55 88 


193 


83.60 


257 


1 1 1. 32 


a 


66 


28.58 


130 


56.3> 


194 


8403 


258 


111.76 


3 


r30 


^l 


29 02. 


131 


56-74 


19s 


84.47 


259 


112.19 


4 


»-73 


68 


29 45 


132 


57.18 


.96 


8490 


260 


112.62 


1 


2.16 


69 


29.88 


»33 


57-61 


197 


S5-33 


261. 


113.06 


259 


70 


30.32 


134 


5804 


198 


85 76 


262 


i'3-49 


1 


303 


71 


30.75 


13s 


5848 


199 


86.20 


263 


113.92 


346 


72 


31.18 


136 


58.91 


200 


86,63 


264 


114.36 


9 


3-89 


73 


31:62 


137 


59-34 


201 


87.07 


265 


114.79 


10 


4-33 


74 


3205 


138 


59.77 


202 


87-50 


266 


115 22 


11 


4-76 


7| 


32-48 


J 39 


60.21 


203 


87.93 


267 


i 15.66 


12 


S20 


76 


3292 


J 40 


60 64 


204 


88. 36 


268 


116.09 


13 


563 


77 


33 35 


141 


61.07 


205 


S8.S0 


269 


116.52 


H 


6.06 


78 


3378 


142 


61.51 


206 


8923 


270 


116.96 


15 


6.49 


79 


3421 


143 


61.94 


207 


8966 


271 


i'7-39 


16 


6-93 


80 


3465. 


144 


62.37 


20S 


90 10 


272 


117 82 


17 


7-36 


81 


3508 


14s 


6281 


209 


90-53 


273 


iiS 26 


j8 


7-79 


82 


35 52 


146 


63.24 


210 


90.96 


274 


118.69 


>9 


S22 


83 


35-95 


147 


6367 


211 


91 39 


275 


119 12 


20 


8.66 


^ 


36.39 


14S 


64.10 


212 


91 -S3 


276 


119.56 


21 


9.09 


fl 


36.82 


149 


64.54 


213 


92.26 


277 


11999 


22 


9 53 


86 


3725 


150 


64.97 


214 


92.69 


278 


12042 


23 


9.96 


ll 


37 68 


151 


65 40 


215 


93 13 


279 


120.85 


24 


10.39 


88 


38 12 


"52 


65.84 


2l6 


9356 


2S0 


121.29 


*l 


J0.82 


89 


38.55 


153 


66.27 


217 


93 99 


2S1 


121.72 


36 


11.26 


90 


3898 


J 54 


66.70 


218 


94-43 


iS2 


122.15 


=^2 


n.69 ; 


9« 


3942 


'55 


67.14 


219 


94.S6 


2S3 


122.59 


28 


12.12 


92 


39-85 


156 


^^57 


220 


95-30 


2S4 


123.02 


29 


»2-5S 1 


93 


40.28 


157 


68.00 


221 


95.73 


2S5 


12345 


■JO 


12.99 i 


94 


40.72 


J58 


^■P 


222 


9616 


2S6 


123.89 


n 


13.42 


95 


41. '5 


159 


6887 


223 


96 60 


2S7 


124.32 


32 


1386 ' 


96 


41.58 


.60 


69-31 


224 


97-03 


2SS 


124.75 


33 


14.29 


97 


42.01 


161 


69.74 


225 


97.46 


2S9 


125. iS 


34 


>4-72. 


98 


"^^ili 


162 


7017 


226 


97.90 


290 


125.62 


3| 


15.16 


99 


42.88 


163 


70.61 


227 


98- 33 


291 


126.05 


36 


'5-59 


100 


4331 


164 


71.04 


22S 


9876 


292 


126.48 


3| 


ic.02 


101 


43-75 


165 


71.47 


229 


9920 


293 


12692 


3S 


iO.45 


102 


44.18 


166 


71.91 


230 


9963 


294 


127-35 


39 


1689 


103 


44.61 


"^l 


72-34 


231 


100.06 


295 


127.7S 


40 


>7-32 


104 


45-05 


168 


72.77 


232 


10c 49 


296 


12S.22 


4> 


17.75 


105 


4548 


169 


73.20 


233 


10093 


297 


12S65 


42 


1.S.19 


106 


45 9' 


170 


7364 


234 


101 36 


298 


129.08 


43 


18.62 


107 


46.34 


171 


■74.07 


23s 


101.79 


299 


129.51 


44 


1905 


loS 


46.78 


172 


7450 


236 


102 23 


300 


129-95 


^i 


^949 


J09 


4721 


173 


74-94 


237 


102,66 


3'o 


134-25: 


46 


1992 


110 


47.64 


.174 


75-37 


23S 


10309 


320 


138.62 


47 


20.35 


111 


48 oS 


17s 


75.80 


239 


103 .i3 


330 


142.9s 


48 


20.79 


112 


48.5^ 


176 


76.23 


240 


103.96 


34« 


147.23 


A9 


21 22 


1J3 


48.94 


'"Z 


76.67 


241 


104.39 


350 


151.61 


S'= 


21.65 


114 


49- .38 


17S 


77 10 


242 


104.S3 


360 


155-94 


5i 


22.09 . ; 


"^ 


4981 


179 


77-53 


243 


105.26 


370 


160.27 


52 


22.52 


116 


.50:24- 


180 


77-97 


244 


105.69 


3S0 


164.61 


S3 


22.9s i 


117 


50 68 


iSi 


78.40 


245 


106.13 


390 


16S.94 


54 


2339 1 


118 


51 11 


1S2 


78.84 


246 


106.56 


400 


17327 


55 


23. S2 1 


119 


51-54 


'S3 


79.27 


247 


106.99 


500 


21658 


56 


24.26 j 


120 


51. 98 


1S4 


7970 


248 


107.43 


600 


259.90 


57 


2469 


121 


52.41 


1 85 


So. 14 


249 


107.86 


700 


303.22 


58 


•25.12 


122 


52.S4 


186 


80.57 


250 


10S.29 


Soo 


iti?. 


59 


25-55 


123 


53-28 


1S7 


81.00 


25' 


108.73 


9^X3 


60 


25-99 ; 


124 


53-71 


iS« 


8.-43 


252 


J 09 16 


1000 


433 i8 


61 


2642 1 


'25 


54- '5 


iSg 


Si. 87 


253 


10959 






62 


26.85- ! 


126 


5458 


190 


82.36 


254 


110.03 






63 


27.29 1 


127 


SS-oi 


191 


8273 


2-55 


110.46 


) 




64 


27.72 ! 


128 


55-44 a 


193 


8.V>7 


256 


iioSg 







_,„,,, From catalogue of Chapman Valve Mfg. Co. 

10 tmd the pressure per sq. in. of a column of water of any height multi- 
ply the height of the column by .43318 (or 434, as it is usually given.) 
See note on next page. 



«5 



Note, as to table on last page. Many suppose that a well 
having a static pressure of a certain number of pounds per 
sq. in. has the same service, duty and volume of delivery as 
would be obtained from a column of water falling through a 
pipe of same size and with a head corresponding to the pres- 
sure of the well. Such is not the case, however, there being 
no known relationship between the two so far as a well is 
concerned. 

To illustrate— From table we see that a head of 231 feet 
will give a pressure of lOO.OH pounds per square inch and 
(although not given in the table) a certain volume will be 
delivered per minute. If either the head, pressure or vol- 
ume be known the other two may be accurately estimated. 
In case of a well, however, this is not true. A well having 
a pressure of 50 pounds per sq. in. may throw more water 
than another well having a pressure of 100 pounds per sq. 
inch and eithei' one may throw either move or less than would 
be delivered from a pipe of the same size having a head of 
116 feet, which corresponds nearly with a pressure of 50 
pounds to the inch. In other words— the volume of a well 
cannot be found by knowing its pressure; nor can the pres- 
sure be found by knowing its volume. The pressure must 
be measured with a gauge and the volume by weiring the 
stream or by some other accepted method. 

EVERY WELL SHOULD BE PEOVIDED 
WITH A GAUGE 
and a proper record preserved of the pressures during differ- 
ent seasons of the year, during different stages of the 
weather and directions of the wiod and during the several 
stages of service of the well. 

Systematic records thus kept would no doubt go far 
toward settling the questions of source and supply. It has 
been claimed, and apparently on good grounds, that the 
standing of the barometer and the direction of the wind have 
a marked effect on both the volume and pressure of some 
wells. No systematic records having been kept of these 
observations it cannot be definitely stated that the fluctua- 
tions in volume and pressure of the wells were due to the 
changes in the weather,but the matter having been suggested 
is one well worthy of attention because of its scientific pos- 
sibilities. 

TABLE NO. 25. 



Diam. of 

pipe in 

inches . 

3 

4 

4.5 
5 
6 
7 
8 



Area in 


Area in 


Gals, in 


square 


square 


900 feet 


feet. 


inches . 


of pipe. 


.0491 


7.07 


.330 


.0873 


12.56 


587 


.1105 


15.90 


743 


.i;m 


19.64 


918 


.1963 


28.27 


1322 


.2673 


38.48 


1799 


.:3490 


50.27 


2350 



Weiglit of 
water in 
900 feet. 



2756 lbs. 

4897 " 

6199 " 

7656 " 

11021 " 

15011 " 

19598 " 



An idea may be 
gained from this ta- 
ble as to the stupend- 
ous energy necessary 
to throw out this vol- 
ume of water at velo- 
cities ranging from 
500 ft. to 2000 feet per 
minute as is done by 
Dakota's Artesian 
WeUs. 



TABLE NO. 26. 
From Trautwine's ^'' Civil Engineer-s Pocket Book.' 



CONTENTS OF CYLINDERS, OR PIPES. 



Contents for one foot in length, in Cub Ft, and in U. S. Gallons of 

231 cub ins, or 7.4805 Galls to a Cub Ft. A cub ft of water weighs about 62^ lbs ; and a gallon 
about 83^ lbs. Ulams 3, 8, or 10 titmes as great, give i, S>, or 100 t'— -- ♦'-" content. 
For the iveig^ht of water in pipes, see Table No. 22 

So errors. 







For 1ft. in 






For 1 ft in 






For 1 ft. in 






length. 






length. 






length. 


Diam. 


Diam. 
in deci- 






Diam. 
in 


Diam. 
in deci- 




Diam. 


Diam. 
in deci- 






in 


. a 


"H 2 


*5.9 


fc. m 


. a 


^. GQ 


Ids. 


mals of 


|rt . 


o a 


Ins. 


mals of 


d)'^ 


o a 


in 


mals of 


% cS . 


o a 




a foot. 


fege 


Sj= 




a foot. 


fege 


a^ 


Ins. 


a foot. 


^f.& 


a.o 






. ee . 


O 3 






• «* ,1 


o a 






. ci ■ 


O 3 






•SgS- 


"32 






■§g« 


•3" 






•§g" 


i" 






o^ 


o« 






«^ 


OS 






^:5 


OS 


H 


.0208 


.0003 


.0025 


% 


.5626 


.2485 


1.859 


19. 


1.583 


1.969 


14.73 


6-16 


.0260 


.0005 


.0040 


7. 


.5833 


,2673 


1.999 


A. 


1.625 


2.074 


16.51 


% 


.0313 


.0008 


.0057 


^ 


.6042 


.2867 


2.145 


20 


1.667 


2.182 


16.32 


7-16 


.0365 


.0010 


.0078 


M 


.6250 


.3068 


2.295 


A. 


1.708 


2.292 


17.15 


}4 


.0417 


.0014 


.0102 


.6458 


.3276 


2.450 


21 


1.750 


2.405 


17.99 


9-16 


.0469 


.0017 


.0129 


8. 


.6667 


.3491 


2.611 


Vi 


1.792 


2.521 


18.86 


% 


.0521 


.0021 


.0169 


17 


.6876 


.3712 


2.777 


22 


1.833 


2.640 


19.75 


11-16 


.0573 


.0026 


.0193 


72 


.7083 


.3941 


2.948 


M 


1.875 


2.761 


20.66 


H 


.0625 


.0031 


.0230 


% 


.7292 


.4176. 


3.125 


23 


1.917 


2.885 


21.58 


13-16 


.0677 


.0036 


.0269 


9. 


.7500 


.4418 


3.305 


Vi 


1.958 


3.012 


22.53 


Ji 


.0729 


.0042 


.0312 


^ 


.7708 


.4667 


3.491 


24 


2.000 


3.142 


23.50 


15-16 


.0781 


.0048 


.0359 




.7917 


.4922 


3.682 


25. 


2.083 


3.409 


25.50 


1. 


.0833 


.0055 


.0408 


VA 


.8125 


.5185 


3.879 


26. 


2.167 


3.687 


27.58 


}i 


.1042 


.0085 


.0638 


10. 


.8333 


.6464 


4.080 


27. 


2.250 


3.976 


29.74 


A 


.1250 


.0123 


.0918 


Va. 


.8542 


.5730 


4.286 


28. 


2.333 


4.276 


31.99 


74 


.1458 


.0167 


.1249 


1/ 


.8750 


.6013 


4.498 


29. 


2.417 


4.587 


34.31 


2. 


.1667 


.0218 


.1632 


74 


.8958 


.6303 


4.715 


30. 


2.500 


4.909 


36.72 


% 


.1875 


.0276 


.2066 


11. 


.9167 


.6600 


4.937 


31. 


2.583 


5.241 


39.21 


i| 


.2083 


.0341 


.2550 


M 


.9375 


.6903 


6.164 


32. 


2.667 


5.585 


41.78 


VA 


.2292 


.0412 


.3085 


A 


.9583 


.7213 


5.396 


33. 


2.750 


5.940 


44.43 


3. 


.2500 


.0491 


.3672 


yA- 


.9792 


.7530 


5.633 


34. 


2.833 


6.305 


47.15 


Va 


.2708 


.0576 


.4309 


12. 


1 Foot. 


.7854 


5.875 


35. 


2.917 


6.681 


49.98 


A 


.2917 


.0668 


.4998 


Vi 


1.042 


.8.522 


6.375 


36. 


3.000 


7.069 


52.88 


74 


.3125 


.0767 


.6738 


13. 


1.083 


.9218 


6.895 


37. 


3.083 


7.467 


55.86 


4. 


.3333 


.0873 


.6528 


Vi 


1.125 


.9940 


7.436 


38. 


3.167 


7.876 


58.92 


'i 


.3542 


.0985 


.7369 


14. 


1.167 


1.069 


7.997 


39. 


3.250 


8.296 


62.06 


.3750 


.1104 


.8263 


Vi 


1.208 


1.147 


8.578 


40. 


3.333 


8.727 


65.28 


% 


.3958 


.1231 


.9206 


15. 


1.250 


1.227 


9.180 


41. 


3.417 


9.168 


68.58 


5. 


.4167 


.1364 


1.020 


y% 


1.292 


1.310 


9.801 


42. 


3,500 


9.621 


71.97 


% 


.4375 


.1503 


1.126 


16. 


1.333 1.396 


10.44 


43. 


3.583 


10.085 


75.44 


i| 


.4583 


.1650 


1.234 


M 


1.375 


1.485 


11.11 


44. 


3.667 


10.559 


78.99 


/4 


.4792 


.1803 


1.349 


17. 


1.417 


1.576 


11.79 


45. 


3.750 


11.045 


82.62 


6. 


.5000 


.1963 


1.469 


Vi 


1.458 


1.670 


12.49 


46. 


3.833 


11.541 


86.33 


^ 


.5208 


.2131 


1.594 


18. 


1.500 


1.767 


1.3.22 


47. 


3.917 il2.048 


90.13 


.5417 


.2304 


1.724 


A 


1.542 


1.867 


13.96 


48. 


4.000 112.566 

1 


94.00 



Table continued, but with the diams in feet. 



Biam. 


Cub. 


u. s. 


Diam. 


Cub. 


U. S. 


Dia. 


Cub. 


U.S. 


Dia. 


Cub. 


U.S. 


Feet. 


Feet. 


Galls. 


Feet. 


Feet. 


Galls. 


Feet. 


Feet. 


Galls. 


Feet. 


Feet. 


Galls. 


4 


12.57 


94.0 


7 


38.49 


287.9 


12 


113.1 


846.1 


24 


452.4 


3384 


1/ 


14.19 


106.1 


A. 


41.28 


308.8 


13 


132.7 


992.8 


25 


490.9 


3672 


15.90 


119.0 


'i 


44.18 


330.5 


14 


153.9 


1152. 


26 


530.9 


3971 


17.72 


132.5 


47.17 


352.9 


15 


176.7 


1322. 


27 


572.6 


4283 


5 


19.64 


146.9 


8 


50.27 


376.0 


16 


201.1 


1504. 


28 


615.8 


4606 


1 


21.65 


161.9 


A 


56.75 


424.5 


17 


227.0 


1698. 


29 


660.5 


4941 


23.76 


177.7 


9 


63.62 


475.9 


18 


254.5 


1904. 


30 


706.9 


5288 


^ 


25.97 


194.3 


A 


70.88 


530.2 


19 


283.5 


2121. 


31 


754.8 


5646 


6 


28.27 


211.5 


10 


78.54 


587.6 


20 


314.2 


2350. 


32 


804.3 


6017 


<4 

A 


30.68 


229.5 


V. 


86.59 


647.7 


21 


346.4 


2591. 


33 


855.3 


6398 


33.18 


248.2 


11 


95.03 


710.9 


22 


380.1 


2844. 


34 


907.9 


6792 


% 


35,79 


267.7 


A 


103.90 


777.0 


23 


415.5 


3108. 


35 


962.1 


7197 



67 
TABLE NO. 27. 

RELATIVE DISCHARGING CAPACITIES OF FULL 
SMOOTH PIPES. 



Dia. 

in 

Feet. 


Relative 

Discharg'g 

Power. 


i 3 

1 


4 


6 


8 


■ 
10 


12 


14 


16 




d 

4. 

3.667 

3-333 

3- 

2.750 

2.500 

2.250 

2. 


32.000 

25750 
20.235 

15.588 

12.541 

9859 
7-594 
5-657 

4-549 
3.588 

2.756 
2052 

1.47 1 

X. 

.6339 
.3629 
.1768 
.0641 
.0312 
















15-59 

12.54 

9.85 

7-59 
6.11 
4.80 
3-70 
2.75 
2.r6 
1.74 

1.34 
I 


48 

44 














17.50 

1347 
8.41 
8.52 

6.54 
5.16 

3-84 
309 
2.43 
1.87 

1-39 
I 






« • • «• 






20.23 
15.58 
12.54 
9.85 
7-59 
5-65 
4-5j 
3-58 

2.75 
2.05 

1.47 

I 


40 












36 
33 
30 
27 
24 








34.55 
27.09 

16.61 

1558 

12.53 
9.88 

565 
4-05 

2-75 
1.74 
I 


19.78 

1554 
996 
8.92 
7.17 
5.66 
4-34 

3-23 
2.32 

1-57 
I 




• • • 


42.95 
32.00 

25-73 
20.29 

15.58 

11.60 

8.32 

S-6q 

3- 58 
2.05 

I 


1-833 
1.667 
1.500 

1.333 
I.167 

1 


65-77 
47.14 
32.05 
20.31 
11.63 
5.66 
2.05 

• 


70.96 

55-96 
42.01 
32.01 
22.94 
15.60 
9.88 
5-66 

2.75 
I 


22 

2C 
18 
16 

14 
12 


.500 

•333 
.250 






10 




... . 




s 

6 












4 

3 





























From J. T. Fanning's "Water Supply Engineering.* 



The foregoing table shows approximately the relative discharging pow- 
ers of pipes of different diameters. In the second column the diameter 1 
foot is assumed as a unit, and the figures show the relative discharging 
value of pipes whose diameter is given in the first column ; for example, a 
pipe four feet in diameter will discharge 32 times as much water as one 
which is one foot in diameter, other things being equal ; a pipe 3 feet in 
diameter 15.588 times as much, one 2J feet in diameter, 9.859 times as much 
and so on. 

The numbers at the intersections of the horizontal and vertical colurnns 
from the diameters in inches give also approximate relative discharging 
capacities. For example, a 48-inch pipe is equal to 15.59, 16-inch pipes, or 
we find that a 24:-inch pipe is equal to 32, 6-inch pipes or 15.58, 8-inch pipes, 
and that a 12-inch pipe is equal to 5.65, 6-inch pipes. 



Note : The relative discharging power as given above is seen to equal 
the square root of the fifth power of the diameter, (df ) To find, there- 
fore, the rel. dis, power for any size not given in this table consult the ta- 
ble of sq. rts. of 5th powers, table No. 69, page 166. 



TABLE NO. 28. 

FRICTION HEADS AND DLSCHAROES. 

For 100 feet of pipe. By Wiesbach's Formula. Trauttvine. 





Vel- 

head in 

Feet. 








Diam. ii 


Inches. 










Vel. in 
Feet 


3 


3^ 


4 


4] 


4 

Cub ft 
perMin 




> 


per Sec. 


Frhead 

Ft per 
100 ft. 


Cub ft 
per Min 


Frhead 
Ft per 
100 ft. 

.565 


Cub ft 
per Min 


Frhead 
Ft per 
100 ft. 


Cub ft 
per Min 


Frhead 
Ft per 
100 ft. 


Frhead 
Ft per 
10© ft. 


Cub ft 
per Mia 


2.0 


.062 


.659 


5.89 


8.02 


.494 


10.4 


.439 


13.2 


.395 


16.3 


2.2 


.075 


.780 


6.48 


.669 


8.82 


.585 


11.5 


.520 


14.6 


.463 


18.0 


2.4 


.090 


.911 


7.07 


.781 


9.62 


.683 


12.5 


.607 


15.9 


.547 


19.6 


2.6 


.105 


1.05 


7.65 


.901 


10.4 


.788 


13.6 


.701 


17.2 


.631 


21.3 


2.8 


.122 


1.20 


8.24 


1.03 


11.2 


.900 


14.6 


.800 


18.5 


.720 


22.9 


3.0 


.140 


1.35 


8.83 


1.16 


12.0 


1.02 


15.7 


.905 


19.8 


.815 


24.5 


3.2 


.160 


1.52 


9.42 


1.31 


12.8 


1.14 


16.7 


1.02 


21.2 


.915 


26.2 


3.4 


.180 


1.70 


10.0 


1.46 


13.6 


1.27 


17 8 


1.13 


22.5 


1.02 


27.8, 


3.6 


.202 


1.89 


10.6 


1.62 


14.4 


1.41 


18.8 


1.26 


23.8 


1.13 


29.4 


3.8 


.225 


2.08 


11.2 


1.78 


15.2 


1.56 


19.9 


1..39 


25.-i 


1.25 


31.0 


4.0 


.250 


2.28 


11.8 


1.96 


16.0 


1.71 


20.9 


1..52 


26.5 


1..S7 


32.7 


4.2 


.275 


2.49 


12.3 


2.14 


16.8 


1.87 


22.0 


1.66 


27.8 


1..50 


34.3 


4.4 


.302 


2.71 


12.9 


2.33 


17.6 


2.03 


23.0 


1.81 


29.1 


1.63 


36.a 


4.6 


.330 


2.94 


13.5 


2..52 


18.4 


2.21 


24.0 


1.96 


30 4 


1.76 


37.6 


4.8 


.360 


3.18 


14.1 


2.72 


19.2 


2.38 


25.1 


2.12 


31.8 


1.91 


39.2 


5.0 


.390 


3.43 


14.7 


2.94 


20.0 


?..57 


2G.2 


2.28 


.3.3.1 


2.05 


40.9 


5.2 


.422 


3 68 


15.3 


3.15 


20.8 


2.76 


27.2 


2.45 


34.4 


2.21 


42.5 


5.4 


.455 


3.94 


15.9 


3.38 


21.6 


2.96 


28.2 


2.63 


35.8 


2..S7 


44.2 


5.6 


.490 


4.22 


16.5 


3.61 


22.4 


3.16 


29.3 


2.81 


37.1 


2..53 


45.8 


5.8 


.525 


4.50 


17.1 


3.85 


23.2 


3.37 


30.3 


3.00 


38.4 


2.70 


47.4 


6.0 


.562 


4.78 


17.7 


4.10 


24.0 


3.59 


31.4 


3.19 


39.7 


2.87 


49.1 


6.2 


.600 


5.08 


18.2 


4.36 


24.8 


3.81 


32.4 


3..39 


41.0 


3.05 


50.7 


6.4 


.940 


5.39 


18.8 


4.62 


25.6 


4.04 


33.5 


3..59 


42.4 


3.23 


52.3 


6.6 


.680 


5.70 


19.4 


4.89 


26.4 


4.28 


34.5 


3.80 


43.7 


3.42 


54.a 


6.8 


.722 


6.02 


20.0 


.5.16 


27.3 


4.52 


35.6 


4.01 


45.0 


3 61 


65.6 


7.0 


.765 


6.35 


20.6 


5.45 


1^8.0 


4.77 


36.6 


4.24 


46 4 


3.81 


57.2 





Vel- 










[)iam. in 


Inches. 










Vel. in 


6 






8 


9 


10 


Feet 


head in 






















per Sec. 


Feet. 


Frhead 
Ft per 
100 ft. 


Cub ft 
per Min 


Frhead 
Ft per 
100 ft. 


Cub ft 
per Min 


Frhead 
Ft per 
100 ft. 


Cub ft 
per Min 


Frhead 
Ft per 
100 ft. 


Cub ft 
per Min 


Fr head 
Ft per 

loeft. 


Cub ft 
per Min 


2.0 


.062 


.329 


23.5 


.282 


32.0 


.247 


41.9 


.220 


53.0 


.198 


66.4 


2.2 


.075 


.390 


25.9 


.334 


35.3 


.293 


46.1 


.260 


58.3 


.234 


72.0 


2.4 


.090 


.456 


28.2 


.390 


38.5 


.342 


50.2 


<304 


6.3.6 


.273 


78.5 


2.6 


.105 


.526 


30.6 


.450 


41.7 


.394 


54.4 


.3.50 


68.9 


.315 


85.1 


2.8 


.122 


.600 


32.9 


.514 


44 9 


.450 


58.6 


.400 


74.2 


.360 


91.6 


3.0 


.140 


.679 


3.1.3 


.582 


48.1 


.5f)9 


62.8 


.453 


79.5 


.407 


98.2 


3.2 


.160 


.763 


37.7 


.654 


51.3 


.572 


67.0 


.508 


84.8 


.458 


105 


3.4 


.180 


.851 


40 


.729 


54.5 


.638 


71.2 


.567 


90.1 


.510 


111 


3.6 


.202 


.943 


42.4 


.808 


.57.7 


.707 


75.4 


.629 


95.4 


.563 


118 


3.8 


.225 


1.04 


44.7 


.892 


60.9 


.780 


79.6 


.693 


101 


.624 


124 


4.0 


.250 


1.14 


47.1 


.979 


64.1 


.856 


8.3.7 


.761 


106 


.685 


131 


4.2 


.275 


1.25 


49.5 


1.07 


67.3 


.935 


87.9 


.8.32 


111 


.748 


137 


4.4 


.302 


1.35 


51.8 


i.ir, 


70.5 


1.02 


92.1 


.905 


116 


.814 


144 


4,6 


.330 


1.47 


54.1 


1.26 


73.7 


1.10 


96.3 


.981 


122 


.883 


1.50 


4.8 


.360 


1.59 


56.5 


1.36 


76.9 


1.19 


100 


1.06 


127 


.954 


157 


5.0 


.390 


1.71 


58.9 


1.47 


80.2 


1.28 


105 


1.14 


1.32 


1.03 


163 


5.2 


.422 


184 


61.2 


1.58 


83.3 


1.38 


109 


1.23 


138 


1.10 


170 


6.4 


.455 


1.97 


63.6 


1.69 


86.6 


1.48 


113 


1..31 


143 


1.18 


177 


6.6 


.490 


2.11 


66.9 


1.81 


89.8 


1.58 


117 


1.40 


148 


1.26 


183 


5.8 


.526 


2.25 


68.3 


1.93 


93.0 


1.68 


121 


150 


154 


1..35 


190 


6.0 


.562 


2.39 


70.7 


2.05 


96.2 


1.79 


125 


1..59 


159 


1.43 


196 


6.2 


.600 


2.54 


73.0 


2.18 


99.4 


1.90 


130 


1.69 


164 


1.52 


203 


6.4 


.640 


2.69 


76.4 


2..31 


102 


2.02 


134 


1.79 


169 


1.61 


206 


6.6 


.680 


2.86 


77.7 


2.44 


106 


2.14 


138 


1.90 


175 


1.71 


216 


6.8 


.722 


3.01 


80.1 


2.58 


109 


2.26 


142 


2.01 


180 


1.81 


222 


7.0 


.765 


3.18 


82.4 


2.72 


112 


2.38 


146 


2.12 


185 


1.90 


229 



See exmaple of use on page 69. 



m 

Example of use of table No. 28. I have 150 lbs. pressure 
at well; 2000 ft. of 3 inch pipe discharging 110 gallons per 
minute. What is the eftective pressure at point of discharge ? 
From table 36 we tind that 110 gals. = 14.7 cu, ft. From ta- 
ble 28, under head of 3 inch pipe, we find 14.7 cu. ft. discharge 
= 5 ft. velocity per sec. and a loss of 3.43 ft. head per 100 ft. 
3.43 X 20 = 68.6 = ft. loss of head in 2000 ft. of pipe. From 
table 24 we find 68.6 ft. head to = 29.7 lbs. of pressure. 150 
lbs. (given pressure)— 29.7 lbs.= 130.3 lbs.= effective pressure 
at point of discharge. 

Further example of use of table 28. 

To get discharge from pipe of given size and length. 

From table 28— within certain limits -may be found the 
volume discharged by a pipe of given size and length, under 
a given pressure. 

Example: A well has a pressure of 78 lbs, per inch, and it 
is desired to convey water to a reservoir through 3000 ft. of 
3 inch pipe; what will the pipe discharge per minute at the 
reservoir ? From table 24 (P. 64.) we find that 78 lbs. = head 
of 180 ft. which head is to be used to force the water through 
30 hundred feet of pipe, therefore gV of 180 = 6 ft. = the 
available head for lOO ft. In table 28 we find, under 3 inch 
pipe, the nearest corresponding friction head which is 6.02 
ft. which corresponds to a velocity of 6.8 ft. per sec. and a 
volume of 20 cubic ft. per minute, which, from table 36 = 
149.6 gallons. (Xo account is here taken of the velocity head 
which is less than I ft. and remains the same for any length 
of pipe; being dependent only upon the velocity in the pipe.) 

Over column two of table No. 28 appears the heading 
" Vel. head in ft.", and over column three appears the head- 
ing " Fr. head ft. per 100 ft." The first is read as Velordty 
head and the second as Friction head. The distinction is 
here explained. 

By Head is meant the vertical distance in feet between the surface of 
the source of supply and the centre of the orifice through which the water 
flows. The total head is divided into 3 parts called, respectively, Entry 
Head- Velocity Head, and Friction Head ; the respective func- 
tions of which are as follows : 

£ntry Head is that portion of the total head used in overcoming the 
resistance to the entry of the water into the pipe. The entry head is less 
as the edges at the point of entry are rounded. It is equal to about one- 
half the velocity head. 

Velocity Head is that portion of the total head used in maintaining 
a certain velocity within the pipe, assuming that there is no friction in the 
pipe. It is therefore equal to the height through which a body would fall 
—in a vacuum— to gain the same velocity as that of the water in the pipe. 

ys ■ 

Expressed as a formula Vel. Hd. = ^r- , in which V'^ = 

'^g 
the square of the velocity in ft. per see. and g = the acceler- 
ation" of gravity, or 32.2. The formula then becomes 

ys 
Velocity Ffead =~arr - or, what is practically the same- 
Velocity or ) _ ( square of vel. ) ^ ^-, -= 
Theoretical Head r "lin ft. per sec. ^ ^ '^^^^' 

The velocity head rarely exceeds 1 ft. and is constant for all lengths of pipe. 



70 

Friction Head is the remainder of the total head; or such 
an amount as is just sufficient to overcome the friction in 
the pipe leaving the remaining head to cause the entry and 
velocity of the flow. The smoother and shorter the pipe is 
the less the friction head will be and the greater the velocity 
head will become. 

The Theoretical Velocity due to any given head is, if ex- 
pressed in a formula — 

S'ft'^plf ''s'e'c^} = s2gir= veOhT in which h = the given 

head in feet. 

This is practically the same as Theor. Yel. = 8.03 times 
the sq. rt. of h. 

Example— What is_the theoretical Tel. under a head of 4 
ft? \64.4 X 4 = v257^ which, from table of roots, = 16.05— 
or— by the second rule, the sq. rt. of h (4 ft.) = 2 which X 
8.03 = 16.06. 

e 

The above explanation will not only explain clearly thg 

significance of the values in table 28 but will also be of us 
otherwise. 

Table 29 is similar to table 28, except that the velocities in 
the pipe are in single feet, and extend to 20 feet, instead of 
in feet and decimals, as in table 28. The values in table 29 
differ slightly from those due to corresponding sizes and vel- 
ocities given in table 28. This difference is due to calcula- 
tions having been made from different formulae, but they 
are too slight to be material since the variations in the pipes 
themselves will cause as great variations— either more or less 
— from the quantities given in either table. 

The limits of tables 28 and 29 are too narrow to suit all the 
conditions of our wells and practice, so a few simple rules 
are given to suit all conditions, these rules, and table 30 upon 
which they are based, being adapted from Haswell's Pocket 
Book. 

It may be added that by reason of varying conditions 
whatever rules or formulae are applied the result will be 
in a measure approximate. 

To find the Friction Head.— Wiesbach's Formula. 

r .01716 ^ Length VeP in 

Friction head_ \ oi44 -f / — r~- — jz ( in feet ft per sec 

in feet ' ) ' vel in tt > x jjj^^ X 64 4 " 

( s/ per sec ) i^ feet 

The use of this formula requires a knowledge of the velo- 
city in ft. per sec. which may be found by dividing the vol- 
ume in cubic ft. per second by the area of the pipe. (See 
page 82.) 



71 



TABLE NO. 29. 
MjOa3 OP BBAD BT FRICTION OF 'WAXFR IN P1PEV. 

CALCULATED FOR PIPES 100 FEET LONG. *^ 





INSIDE DIAMETER OF PIPE 


IN INCHES. 1 


Velocity 

of 
Water 

through 
Pipe in 
Feet per 
Second. 


3 


4 


5 


6 


1 


8 


02. 

o W 

: 5' 


a.-> 
' 


I g 

: 5* 


« ? 

V 

a.~> 


3 -, 


• F 


n 
0.0 



i'2. 


n 

: 2 

i 3 


n ? 

U 

Q.O 

^? 


§2. 


(t n 

■ ? 


(* ? 

I?. 


og. 

n n 

• ? 


<» p 

Q-o 
a.-» 

«? 


.074 


1 


2-95 


.196 


522 


•X47 


8.17 


.118 


11.77 
23-54 


.098 


16.03 


.084 


20.88 


2 

3 


5.89 


•659 


10.44! -494 


16.34 


.395 


-329 


32.05 


.282 


41.76 


.247 


8.83 


1-35 
2.28 


15-67 


1.02 


24.51 


.815 


35-32 


■679 


48.08 


.581 


6264 


•509 


4 


11.80 


20.89 


1.71 


32.69 


1-37 


47-09 
58.87 


1.14 
1.71 


64.11 


.977 


83.52 


.856 


5 


14.70 
17.70 


3-43 


26 12 


2-57 


40.87 2.05 


80.15 


1-47 


104.40 


1.28 


6 

... , 1 

1 


4-78 


31-34 


3-59 
4-77 


49-05 


287 


70.64 


2-39 


96.18 


2.05 


125.28 


1.79 


20.60] 6.35 


36-57 


57.22 


3.8r 


82.41 


3-18 


II2.2I 


2.73 


146.16 


2.39 


8 


23.56 8.14 

1 


41-79 


6.11 


65.40 


4-89 


94.19 


4.07 

5-06 


128.24 


3-49 


167.04 


3.06 

3.79 
4.62 


9 


26.51 


10.12 


47.02 


7-59 


73-57 


6.07 


10597 


144.27 


434 


187.92 
208.80 


10 


i 29-45 


12.32 


52-24 


9.24 


81 -75 


7.39 


117-74 


6.16 


160.30 


5.28 


11 


32.40 
35-34 


14.71 


57-47 


11.03 


89.92 8.82 
98.1010.38 


12952 


7-36 


176.34 


6.31 


229.68 


5.53 


12 


17-31 


62.70 


12.98 


141.30 


8.65 


19237 


7-41 


250.56 


6.49 
7.54 


13 


38-33 


20.10 


67.92 


15.08 


1 
106.27 12 06 


153-07 


10.05 


208.40 


8.61 


271.44 


14 
15 


41,23 
44.20 
47.12 


23.12 


73-15 


17-34 


114.45 13-87 


164.85 


11.56 


224.43 


9.91 


292.32 


8.67 


26.32 


78.38 


19-74 


122.62 15.79 


17663 


13.16 
14.86 


240.46 


11.28 


313.20 


9.87 


16 


29.7^ 


, 83.60 


22 29 


130.80 


17-83 

20.00 


188.40 


256.48 


12.74 


334.08 


11.15 


17 


50.05 


33-33 


88.83 


25.00 


138.97 


200.18 


16.67 
18.57 


272.51 


14.29 


35496 


12.50 


18 


53-00 


37-14 


94.05 


27.86 


147.1522.29 


211.96 


288.54 


15.92 


375.84 


13.93 


19 


55 95 


41. 12 


99-28 


30.84' 


155.3224.67 


223.73 
235.51 


20 56 


304.57 


17.6a 


417-60 


15.4a 


20 


58.89 


45-32 


104.50 


33-99 


163.5027 (« 


23.66 


3ao.6o 


t9-4a 


17.00 



72 



TABLE "SO. 30. 



TABLE AND RULES. 



From Ha swell. 



Diameter 
inches. 


Tabular No. 


Diameter 

inches. 

7 


Tabular No. 1 


1 


4.71 


612.32 ! 


IH 


8.48 


8 


854.99 ! 


m 


13.02 i 


9 


1147.61 


1?4 


19.15 


10 


1493.5 


2 


26.69 


11 


1894.9 


2A 


46.67 


12 


2356.0 


3" 


73.5 


13 


2876-. 7 


3i 


108.14 


14 


;H63.3 


4 


151.02 


15 


j 4115.9 


4i 


194.84 


16 


4836.9 


5 


263.87 


17 


5628.5 


6 


416.54 


18 


6493.1 



APPLICATION OF THE TABLE. 

I. To <'ompiite Volume Discharged— Length of Pii^e, Diam- 
eter, and Fall or Head being given. 

Rule— Divide the tabular number, opposite to the diameter of the pipe, 
by the square root of the rate of inclination (head), and the quotient will 
give the volume required in cu. ft. per min. 

Example— A pipe has a diameter of 4 inches, a length of 2982 ft. and a 
head of 123 pounds pressure (284 ft.) What is the discharge per min.? 

/????=s 105=3.24, and tabular number for 4 in. = 151.02. 
nI 284 ^ 

then, ^^^^^^^ =46.6 cu. ft. per min. = (from table 36) 119 68 gals 

If head, aa in above case, is mpoiinds pressure reduce it to 
feet by reference to table 24; but if pipe is not connected 
'with the well, and the pressure is due to gravity alone, then 
the head will be the vertical distance between the upper and 
the lower ends of the pipe. Reduce volume in cubic feet to 
volume in gallons by reference to table 36. 

II. To comxmte the Diameter necessary to discharge a 
given Volume— the Kead and Length being given. 

Rule — Multiply the given volume by the square root of the ratio of the 
inclination— head — ; take the nearest corresponding number in the table, 
and opposite to it is the diameter required. 

Example— A pipe has a length of 2982 feet, the head is 123 lbs., (284 ft.) 
What size of pipe will it require to discharge 46.6 cubic feet (119.68 gals.) 
per minute? 

46. 6x |????=46.6x3.24=150.98. The nearest tabular num- 
■>/ 284 
ber= 151.02 opposite which is 4 inches = required size. 

III. To compute the Head— the Length, Diameter and 
Volume of discharge being given. 

Rule— Divide the tabular number for the given diameter by the given 
discharge in cu. ft. Square the quotient, and divide the length of the pipe 
by it ; the quotient will give the head necessary to force the given volume 
per minute through the ^ipe. 

Example— What head in ft. (or pressure in lbs) wiU. be required to cause 
a discharge of 46.6 cu. ft. (119.68 gals.) of water per minute from 2982 ft. of 
4 in. pipe? 

?4i^=3.24; 3.24^ = 10.5; 2982^10.5 = 284 =required head in 
46 . 6 

feet which = 123 lbs. pressure. 



73 
\ TABLE NO. 31. 

HORIZONTAL AND VERTICAL DISTANCES REACHED BY JeTS. 



O ii 


Head in lbs. per sq. in. .. 


Pressure at Nozzle. 


5 N 

a o 


20 
46.2 


30 
.69-3 


40 
92.4 


50 


60 
138.6 


70 
161.7 


80 

1S4.S 


90 
207.9 


too 

231.0 






1 

1% 


i Gallons discharged 

{ Horizontal distance of jet 
( Vertical 

( Gallons discharged 

\ Horizootal distance of jet 
( Vertical 

f Gallons discharged 

} Horizontal distance of jet 
( Vertical 

( Gallons discharged 

\ Horizontal distance of jet 
( Vertical 


XIO 

70 

43 

131 
7> 
43 

171 
73 
43 

207 
75 
44 


134 
62 
170 

63 

210 

f 

253 
100 

65 


'55 
109 

79 

196 

81 

242 
ii8 

82 

293 

8S 


126 
94 

219 
132 
97 

99 

327 
146 
102 


189 
142 
loS 

240 
148 
1.12 

297 
'56 
"S 

3S.S 
166 
118 


20s 
'S6 
121 

259 
163 

'25 

320 
172 
129 

3S7 

1^4 

IJ3 


131 

277 

'75 
'37 

342 
1S6 
142 

4'3 
200 
146 


232 
17S 
140 

294 
1S6 
148 

19S 

'54 

439 
213 

'58 


14S 
310 

»91 
»S7 

3Sj 
207 
164 

462 
224 
169 



FROM FANNING'S "WATER SUPPLY' 



To calculate th.e altitude reached by jets. 

^ 8XD / 



S in which A = altitude required, H = head on jet in 
} feet, and D = diameter of nozzle in inches. 



Example — What will be the altitude of a jet discharged from a IV2 inch 
nozzle under a head of 80 pounds pressure? 
(The head being given in lbs. reduce it to feet by multiplj'ing by 2.311— 
1 pound per sq. in. equalling 2.311 ft. of head.) 

80 lbs. X 2.311 - 184.88 = head in feet. 

Then A = 181.88- (lM:^^!>i:^l^) =119.28 ft. altitude. 
^ 8 Xl.o ^ 



To calculate discharge of jets in gallons per minute. 

r>—.rS^sy iQ T\\2 XX n ooo S ^^ whlcli Cr^discharge in gals, per min. H = 
tr-VM X (» L>) X 0.^88 | t^g^d of jet in ft. D=diam. of nozzle in inches 

Using above example. What will be the discharge per min. from a VA 
inch nozzle under a head of 184.88 feet. (=80 lbs. pressure) 



V'H =vl84. 88=13.597 and (8 0)" = (8X1.5) 2 = 144. 
Then formula becomes G= 13.597x144x0.288 which=563.S9 gallons per 
minute. In this way the volume of a well may be calculated very closely. 
Table No. 38, page 89 gives the discharges from different nozzles, under 
different heads, as calculated by this formula. 



74 



SOURCE AND SUPPLY. 

"Where does the artesian water come from?" has been 
asked a thousand times, but has, as yet, received no answer, 
other than a purely theoretical one. Nor can any answer 
be given until a careful geological survey has been made of 
this state and those adjoining it; and until some systematic 
investigations are made in the field of the wells themselves. 
When more wells have been drilled, so that the influence of 
one upon another may be ascertained, or when a series of 
purely experimental wells shall have been drilled by the U. 
S. government, we may then learn something as to the direc- 
tion of the flow and its source. A carefully prepared series 
of analyses, too, may aid in leading the way to the true 
source. There is infinite room for investigation, and noth- 
ing bui roovi as yei provided for the investigator. The 
past season witnessed the taking of the first step leading to 
the determintion of the source of these subterranean waters. 

Considerable work in the way of geological study and sta- 
tistical investigation was done by the several members of 
the committee of Artesian Underflow, and Irrigation Inves- 
tigation, acting, by authority of Congress, under the De- 
partment of Agriculture. 

Without entering into any consideration of the many 
facts upon which this committee of experts based its opin- 
ion, as expressed in its reports to Congress, I state briefly 
the conclusion reached by them as to the probable source of 
this vast subterranean sea. As is well known, the water is, 
in all cases, found in the layers of more or less porous and 
soft sand-rock which underlies nearly the whole state and 
extends thence westward, finally to find an outcropping 
among the eastern foothills of the Rocky Mountains, and 
transverse to the courses of most of the large rivers which 
find a head in that vast drainage area. 

Many observed facts of great weight would tend to 
prove that the vast quantities of water known to be lost 
to the Missouri, the Yellowstone and other large rivers, 
while flowing over the upturned edges of this outcropping 
sand-rock, is carried through these porous sponge-like for- 
mations to find a lodgement beneath the broad acres of Da- 
kota, and an outlet, no one knows where. In the absence of 
any theory having the support of better evidence and a 
greater array of facts in its support this theory as to the 
source of the artesian waters will stand. There seems to be 
little doubt as to its correctness. Assuming it to be correct 
that the fountain head of our wells is in the vast water-shed 
of the Rockies and that the volume supplied to this great 
underground river is what it is calculated to be, the demon- 
stration is complete that the supply is absolutely inexhaus- 
tible for all time and under whatever tax it may serve this 
or future generations. 



75 

I In no case has a well failed 

'or shown any decrease in its volume, provided it has been 
kept clean and open. Some wells have become closed en- 
tirely but when cleaned out they have again flowed with 
their old time vigor. 

What the thickness or depth of the water-bearing sand- 
rock is, has not been determined for no drill has yet gone 
through it. Several wells have been sunk from 50 to 75 feet 
into this rock but the flow has then become so powerful as 
to prevent further drilling. It would be folly indeed to sup- 
pose that the feeble eflforts of man to gain a little water for 
his use would have any effect upon the vast sea of water be- 
neath us the area of which is measured by hundreds of miles 
and the depth by hundreds of feet. All the water that 

ALL THE WELLS IN DAKOTA CAN THROW FOR A HUNDRED 
YEARS WOULD, IF GATHERED TOGETHER, EQUAL A LESSER 
VOLUME THAN NOW UNDERLIES A SINGLE COUNTY— BROWN. 

Figure it out. This is no guess. 
In conclusion I quote from a letter written by Col. E. S. 
Nettleton (The Chief Engineer of the Department of Irriga- 
tion Inquiry, of the U. S. Department of Agriculture.) to 
Mr. K. O. Richards of the Consolidated Land and Irrigation 
Co. of Huron, S. D. 

Col. Nettleton says: 

" In reply to your request for an expression of opinion con- 
cerning the extent and durability of the Dakota artesian 
water supply for irrigation purposes, I will state that after 
two seasons spent in^examining the artesian wells in South 
Dakota, and their probable source of supply, we have come 
to the conclusion that the supply comes from the elevated 
and mountainous country lying to the west (principally in 
Montana), where the rock strata are turned up so as to come 
to the surface. The water is transmitted through and is re- 
tained in the sand rock, which is estimated to be several 
hundred feet in thickness, and is made up of layers (more or 
less fractured) from one to fifteen feet in thickness, and of 
variable degrees of hardness and porosity. Below the strata 
are thin layers of impervious clay, shale, soft sand and lig- 
nite. This formation is exposed and is capable of imbibing 
a large amount of water from the unfailing supply from the 
mountains and the mountain streams and rivers, which have 
cut their way deeply into the artesian water bearing rock. 
I therefore conclude the supply will never fail. It is natural 
to suppose that the artesian supply can be found along the 
entire line between the source of supply and the present ba- 
sin, which has an extent, north and south, of about 425 
miles. I am of the opinion that the deeper the water bear- 
ing strata are penetrated the greater will be the volume ob- 
tained." E. S. Js ETTLETON. 



76 
Artesian Water and Vegetation. 

Before irrigation was thought of in Dakota, and the water 
used upon grains, the opinion was frequently expressed that 
artesian water would injure house plants and trees and 
would kill grass. Experience has disproved all of these 
statements for the most delicate house-plants now thrive on 
this water, the finest lawns in our towns are sprinkled with 
it. Of field grains and garden truck the same is true. Where, 
without its use the plant would die, with its use— and abund- 
ant use — there is such an abundant growth as to astonish the 
grower. Plant growth is a chemical process and the plant 
itself a chemical creation brought about in the laboratory of 
the earth and through the agency of the air and water; the 
latter being nature's great solvent and reagent. From the 
air the plant derives its supply of nitrogen and oxygen, and 
from the water its supply of hydrogen, and, through the sol- 
vent action of water, its supply of lime, soda, potash, mag- 
nesia, iron, manganese, silica, chlorine and other chemicals 
all of which are indispensable to plant life. Different plants 
require different chemical ingredients in their food and ab- 
sorb, of the same ingredient, different proport ons. 

Many analyses have been made of artesian waters and in 
no case has any showing been made of any chemical constit- 
uent of the waters that would be in any way injurious to 
plant life but, on the contrary, the result has shown that the 
artesian water was especially well adapted to the fertiliza- 
tion of our soil and the production of such plants and grains 
as are best suited to our soil and climate. 

The analyses of this water show 



Silica 

Sulphate of sodium 
" " potassium 
" " calcium 
" " magnesia 
" lime. 



Alumina 
Carbonate of lime 
" '• iron 

Chloride of sodium 
Traces of organic matter 
phosphates. 



which elements are in varying quantities according to the 
location of the well. 

The waters of the northern wells are mry soft and this is 
true of some of the southern wells, but, as a rule, the south- 
ern well waters are harder and not so well adapted, on that 
account, to household uses. The taste varies greatly but in 
all cases the water is palatable when cold and it is used by 
thousands of families for drinking in preference to any other 
waters. When warm— as when it'flows from the well— it, in 
some cases, has a brackish, saline, unpleasant taste; but on 
cooling this disappears. The temperature ranges from 55° 
to 68'. In the winter it will run in ditches for several miles 
before freezing and ponds of it will remain open when the 
temperature ranges from 10° to 40 below zero for a week or 
two. This warmth imparted to the soil in the spring forms 
a valuable supplement to the warmth of the sun, quickens 
the act of germination and aids much in the early stages of 
growth. 



77 

THE POWER OF WELLS. 

It is not alone for irrigation and domestic use that the ar- 
tesian waters will be used but also for POWER. The first 
well at Aberdeen, in 1882, demonstrated the possibility of 
utilizing the pressure of the well for the purpose of forcing 
the water through water mains, thus furnishing a system of 
water supply and fire protection second to none in point of 
efficiency and equalled by none in economy of management 
and maintenance. No steam fire engine is necessary to force 
a stream through the mains and hose and over the highest 
buildings; nor is it necessary to provide for the care and 
maintenance of such an expensive plant as is necessary 
with a steam power plant. The first cost of the well was 
less than the cost of an engine, and it fills the double pur- 
pose of supplying the water and forcing it wherever it may 
be needed; and all this at no expense other than an occasion- 
al repair to pipe or valve. 

Few there are, no doubt, in the many towns of Dakota, 
where there are systems of artesian water works, who ever 
pause to consider what these towns would have been had it 
not been for these wells; or what they would have done for 
public fire protection or for domestic consumption but for 
these wonderful "spouters." 

There is no other source adequate, other than to the Mis- 
souri river towns, except to an occassional town, where 
large surface wells, in sand formations, might have supplied 
a very limited public service. The wells have been a God- 
send indeed. The application of the well's pressure to fire- 
pressure service, led naturally to the idea of using it for 
power to run water motors. 

The first application of well power to the operation of 
machinery was by the Aberdeen Electric Light Co. They 
tapped the main pipe of the city's well with a % inch pipe 
and with this stream they ran the entire plant for some 
time. This power was, in the end, abandoned because the 
sand in the water cut out the buckets of the motor. 

At this time there was a move made to build a flour mill 
to be operated by artesian power, but the project was aban- 
doned upon the advice of several eastern hydraulic engineers 
to whom the matter was submitted by the author. Each 
declared it to be impracticable— impo'ssible— to utilize the 
power of these wells, and such expressions of opinion are, 
even now, common among that class of experts; and little 
credence is given to what has since become a demonstrated 
fact. 

Soon the use of small motors became quite common, and 
to-day scores of motors of different makers are used to run 
coffee mills, feed mills, printing presses, elevators and simi- 
lar classes of machinery. The first application of well pow- 
er to the running of a flour mill was at Hitchcock, Beadle 
county, S. D., where, with a small well ^% inches at the bot- 



78 

torn, they run a mill grinding from 40 to 50 barrels of flour 
per day. The motor is a simple, home-made wheel and the 
efficiency fully up to what could be desired from an expens- 
ive steam plant. The saving in tliis instance is not alone 
the cost of fuel, oil, engineer's salary, expensive repairs to 
boiler and engine, etc, etc., but also the decreased danger 
from fire and explosion and the consequent reduction in fire 
insurance rates. The saving in insurance alone will fully 
cover all the expense of operation by the well power. 

This small well also supplies the domestic use and fire 
service of the town, and the exhaust water from the mill 
serves to irrigate a large farm. 

Where on earth, outside of this artesian valley, can an- 
other showing be made that will compare with this ? (See 
page 81.) 

A larger mill at Woonsocket, using a Pelton wheel, runs 
at a capacity of 100 barrels per day. (See page 81.) Other 
mills at Springfield, Yankton and other points also use wells 
for their motive power. All the machinery in the "Huron- 
ite" publishing house, at Huron, S. D., is run by a Chicago 
Water Motor connected to the city water mains; and the 
electric light plant, operating both arc and incandescent 
lamps, is rlin by a 3 foot Pelton wheel connected directly to 
a f)% inch well, which also supplies water to the w^ater 
works. 

A plant, unique in this field and having, to the engineer, a 
greater degree of interest than any other, because of the 
manner of applying the water and the results accomplished, 
is, the sewer plant at Aberdeen. This was the first applica- 
tion of a well to the performance of heavy duty and it is the 
only plant of its kind on the globe. The well is 4>^ inches 
at the bottom and 6 inches at the top, and has a volume of 
about 1500 gallons per minute, under a pressure of from 140 
to 160 pounds to the inch. 

The water is supplied through 3-inch pipes to two Worth- 
ington water motors and pumps. The application of the 
water to the pistons in the cylinders being the same as with 
steam in the cylinders of a steam engine — the water operat- 
ing the same as the steam. 

When the two pumps are running at the rate of 60 strokes each per min- 
ute there is a reserve of pressure at the well of 40 pounds per inch. The 
pumps running at this rate have a capacity of 2,500,000 gallons per day of 
sewage pumped a vertical distance of 23 feet. When on their tour of in- 
spection the U. S. Senate committee on irrigation investigation pronounc- 
ed this plant to be the most wonderful adaptation of the powers of nature 
that had come under their observation. 

Any man who believes that a well cannot be successfully harnessed to a 
load needs but to witness the operation of this plant to be convinced that 
he is in error, for when a well, through the agency of proper machinery, 
will lift a load of twenty millions of pounds a day through 23 feet, or 479 
millions of pounds one foot high in a day, that well may be fairly said to 
have performed a good day's WORK. 

Experts to the contrary, the artesian weUs of Dakota supply the most 
wonderful power on the globe. The stupenduous unutilized, and to a 
great extent, unavailable power of mighty Niagara must pale in compari- 
son with the power of Dakota's artesian wells. 



79 

Here no special mill site must be chosen and then pur- 
chased of the owner at his own figures, for every inch of our 
broad domain is as good a mill site as there is on the earth. 
The ground here has but to be opened in order to pour forth 
the flood which will serve not one purpose alone but many. 

Power, domestic use, fire protection, irrigation, and even 
heat are but the chief among the many duties to which a 
well may be called. More there ar^ which will soon find a 
place in the every day economy of Dakota life; and all com- 
bined will soon be the chief factors in making this the won- 
derland of America. 

Every well owner who can afford it should have a motor, 
for with it much labor of the farm may be performed. A 
very small expense, added to a little ingenuity and home la- 
bor, will harness the churn, the feed mill, the fanning-mill, 
the feed-cutter, the threshing machine, the grindstone and 
other farm machines to the motor and thus save a vast 
amount of labor, expense and even life itself. Any farmer 
will appreciate the great advantage of having his threshing 
done by water power instead of by steam power, in which 
latter case there is the constant danger from fire and explo- 
sion. 

All these things will come, in time, for Dakota's farmers 
are too enterprising to long delay the utilization of the 
forces thus gratuitously laid at their feet. Lack of means 
is the only obstacle to the proper utilization of that which, 
ere long, will transform Dakota into the most productive, 
prosperous, wealthy, and wonderful agricultural region in 
this or any other land. 

JS^or will capital long hold back when it has been fully 
assured oi the successes already achieved by the pioneers in 
the field of irrigation and the development of artesian pow- 
er. No more profitable investment can be found to-day than 
such as is made in Dakota lands on which wells are placed, 
or in the development of this inexhaustable power that 
flows not to wreck and to ruin but to fructify and enrich. 
It becomes, then, the duty of every lover of Dakota to her- 
ald the great truths (unembellished by any exaggerations) as 
to the wonderful possibilities that we ourselves have but 
just begun to appreciate. 

The ear of capital will be reached if we but call long and 
loudly, and when reached the means will cease to be the ob- 
stacle to success which now awaits us. 

On page 81 will be seen the reports of some of the millers 
of the state as to the service rendered them by artesian 
wells. In the face of such facts no argument need be given 
to prove the great value to Dakota of this great source of 
power. The reports are from points widely separated which 
shows the extent of the field. 



80 



TABLE FOR CALCULATING THE KOR.SE POWER 

OF WATER. 

The following^ table gives the horse power of one cubic 
foot of water per minute under different heads. 

TABLE NO. 32. 

Adapted from Pelton Water Wheel Co. 



Heads in 
feet. 



1 

20 

•SO 

40 

50 

60 

70 

80 

90 

100 

110 

120 

130 

140 

150 

160 

170 

180 

190 

200 

210 

220 

230 

240 

250 

260 

270 

280 

290 

300 



Pressure per 
Sq. inch, lbs. 



.43 

8.66 

12.99 

17.32 

21.65 

25.99 

.30.32 

;it.65 

:38.98 

43.31 

47.64 

51.98 

56.31 

60.64 

64.97 

69 31 

73.64 

77.97 

82.30 

86.63 

90.96 

95.;30 

99.63 

103.90 

108.29 

112.62 

116.96 

121.29 

125.62 

129.95 



HoT"se 
Power . 



.0016098 

.032196 

.048294 

.064392 

.080490 

.0965^8 

.112686 

. 128784 

.144892 

.1609^1) 

.17707S 

.193176 

.209274 

. 225372 

.241470 

. 257568 

. 273666 

. 289764 

.305862 

.321960 

.338058 

.354156 

.370254 

.386352 

.402450 

.41X54S 

.434646 

.450744 

.466842 

.482940 



Heads in 


Pressure per 


feet. 


sq. inch, lbs. 


310 


i;U+ 


320 


138 


330 


143 


340 


147 


350 


152 


360 


156 


370 


160 


:380 


164 


390 


169 


400 


173 


410 


178 


420 


182 


430 


186 


440 


191 


450 


195 


460 


199 i 


470 


204 


4S0 


208 


490 


212 


500 


216 


520 


225 


540 


234 


560 


243 j 


580 


251 i 


600 


260 


650 


282 


700 


:i03 


750 


325 


800 


346 


900 


390 



Horse 
Power. 

.4990:38 
.5151:36 
.5:312:34 
.547:3:32 
.5634:30 
. 579528 
.595626 
.611724 
.627822 
.64:3920 
.660018 
.676116 
.692214 
.708:312 
.724410 
.740508 
.7.56606 
.772704 
.78S802 
.>.049i)*( 
.8:57096 
.869292 
.901488 
.9:3:3684 
.965880 
1.04t)370 
1.126860 
1.207:350 
1.287840 
1.448820 



AVhen the !Exact Head is found in tlie Table. 

Example— Have 100 foot head and 300 cubic feet of wa- 
ter. How many horse power have I ? 

From table— H. P. for 100 ft. head=. 160980 for 1 cu. ft. of 
water, hence .160980x300=48.294 the H. P. for 300 cu. ft. per 
minute. 

From table 36 we find that 300 cu. ft. =2244 gallons. 

If a well having a flow of 2244 gallons per minute will, 7MhUe 
tln'oioing that amount, show^ a pressure of 43 lbs. per inch 
(=100 ft. head) then it will develop 48.29 effective horsepower. 

'When Exact Head is not found in the Table- 

Take the H. P. of 1 cu. ft. under 1 foot head and multiply 
by the number of ft. head given, then by the number of cu. 
ft given. The product will be the required H. P. 

Note — The table is based upon an efficiency of 85 per cent. 

Note the fact that a well shows no pressure, w head, when discharging 
its full volume. TTirn it off a little so as to get some pressure, then meaa- 
ure volume and proceed according to above table to calculate the power. 

See page 82. 



81 
W00N80CKET MILL. 

Northy and Duncan of the Wood socket mill report as fol- 
lows: Our well is 775 feet deep; 7 inches in diameter all the 
way; pressure 135 lbs. when closed; 62 lbs. with a 4-inch 
opening, 75 lbs. with a 3-inch opening. We use a 3 foot 
Pelton wheel, lunning at 275 revolutions per minute, the 
nozzle throwing a 1% inch stream. We have made 88 bar- 
rels of flour and 36 tons of good feed per day of 24 hours, 
and we figure on a saving of from $14 to $17 per day as com- 
pared with steam power of equal service. The element of 
safety being worth much that cannot be expressed in figures. 

SPRINGFIELD MILL. 

Mr. J. J. Kattleman of the Springfield mill reports as fol- 
lows: Our well is 593 feet deep; and 8 inches all the way. 
The pressure, when closed, is 80 lbs., and when mill is run- 
ning it is 40 lbs. We use a 16-inch turbine wheel, making 
about 800 revolutions per minute. The well cost $8,000, but 
could be drilled for less now. We put out about 60 barrels 
of fiour per day, and figure on a saving of from $12 to $15 
per day as against steam power. This item alone being a 
handsome profit or interest on the cost of the well. * Repairs 
are very light and insurance much less than with steam. 
We get over 42 horse power from the well. 

YANKTON-'TOUNTAIN " AND "EXCELSIOR" MILLS. 

Mr. E. Miner of the Fountain Roller Mills of Yankton says : WeU is 600 
feet deep, 6 inches in diameter, pressure from 48 to 56 pounds per inch, and 
flows from 1600 to 2000 gallons per minute. We use a Dubuque turbine wheel 
12 inches in diameter and of guaranteed 27 horse power. The cost of the 
power plant, complete to run, was about $4,000. We pay 3 per cent insur- 
ance and would pay 414 or 5 if running by steam. I think we are 
saving over $8 per day as compared with an engine. Our mOl is one of 40 
barrel capacity. 

F. L. Van Tassell of the Excelsior Mill Co., says : Our well is 500 ft. deep, 
pipe 8 inches to the bottom; pressure when closed 52 lbs., with 1 inch 
opening 48 lbs., with 2 inch opening 42 lbs., with 4 inch opening 20 lbs. ; 
water clear and hard. We use a PELTON wheel 6 feet diameter with 25£ 
inch nozzle, revolutions, 125 per minute. Power about 30 horse. We run 
our elevator and raise about 500 bushels of wheat per hour, shell 100 bush- 
els of corn and grind 4000 lbs. of feed per hour. Will soon attach all the 
mill machinery to the well. The well flows 3000 gallons per minute, and, 
with wheel, power house, etc., cost about $4,000. Cost of running it prac- 
tically nothing, so saving per year as compared with steam power is very 
great. 

HITCHCOCK MILL. 

Mr. M. B. Potter of the Hitchcock Milling Co., says : Size of well 4 inches 
at top, 3 inches at the bottom. Depth 960 feet. Volume 1240 gallons per 
minute. Pressure when closed 155 pounds. With 1 inch opening 140 
pounds. With 2 inch opening 82 pounds. We get about 30 horse power 
from a wheel of our own design, it being 50 inches in diameter and runs 
at about 300 revolutions per minute. The well cost the town $4,500. We 
have had no expense for repairs since putting in the wheel in June, 1890 
— nearly 3 years. The mill has a capacity of .50 barrels in 24 hours. Be- 
sides Yunning the mill the well supplies water to the town, maintains 
water in an artificial lake, and waters an irrigated farm. The well has 
been running since 1886 and the volume is invariable and apparently inex- 
haustible and the pressure is uniform. 



82 
HOESE POWER. 

A horse power issiich a power as will raise 33,000 pounds 
one foot high in one minute of time. The term is one of 
mechanics and does not fairly represent the power of the 
average horse which is only about two-thirds as much. 

To calculate the horse power of falling water multiply to- 
gether the number of cubic feet of water falling per minute, 
the vertical distance (head) through which it falls, and the 
number 62.3 (approximate weight of 1 cubic foot of water) 
and divide the product by 33000. 

Example — A well discharges 800 cubic feet per minute 
from a pipe 16 feet above the surface, what is the horse 
power of the well ? 

800 cu. ft.Xie ft. X 62.3 lbs, 797440 
Here, 33,000 " 33000 ~^'^^ ^•^* 

This is the theoretical H. P. The actual H. P. as realized 
from machinery will be less because the wheel or motor 
does not realize' the full efficiency of the water. The per- 
centage of efficiency realized will depend on the form of the 
wheel and the skill of the makers. It will range from 25 to 
90 per cent, of the full power. Turbine wheels realize from 
75 to 85 .per cent, of the power and impact wheels about the 
same amount. 

The table on the next page will prove of value in this con- 
nection. 

TO GET THE VELOCITY OF THE FLOW OF A WELL. 

If the volume has been accurately measured. 

Divide the volume of the flow, in gallons, by the volume in 
gallons contained in one foot of the pipe of the well (=the 
area of the cross section of the pipe). The answer will be 
the velocity in feet per minute. 

Thus— Suppose a 6-inch well throws 1836 gallons per min- 
ute, what is its velocity of discharge in feet per minute ? 

From table No. 26 we see that 1 foot of 6-inch pipe con- 
tains 1.469 gallons. How many feet, therefore, will it take 
to hold 1836 gallons ? 1836-^1.469=1250=the number of feet 
necessary to hold 1836 gallons, or the length of the column 
of water thrown out each minute, or the velocity in feet per 
minute. 1250-^60=20.8, the velocity in feet per second. 

This is the same as the rule for finding the velocity of any 
stream, viz : Divide volume per minute by area of section to 
get velocity per minute, and divide this quotient by 60 to get 
velocity per second. 

To Compute the Volume of Discharge per Minute. 

Rule — Multiply the area of the wet section in sq. ft. by 
the velocity in feet per second to get volume in cubic ft. per 
sec. Multiply this product by 60 to get the volume per min. 
To Compute the Height of the Head in Feet. 

Rule— Divide the volume in cu. ft. per second by the 
area, and the square of this quotient, divided by 64.33, will 
give the height of the head in feet. 



83 



TABLE NO. 33. 

TABLE SHOWIN^G FLOW PER MINUTE EQUAL TO 
A GIVEN FLOW PER DAY AND TOTAL FLOW 
PER DAY FROM A GIVEN FLOW PER MINUTE. 

Netv. 



Total gallons per 


Equal gallons 


Gallons per 


•Equal gallons per 


day. 


per minute. 


minute. 


t day. 


100 


.07 


.1 


144 


200 


.14 


.2 


288 


300 


.21 


.3 


432 


400 


.28 


.4 


576 


500 


.:?5 


.5 


720 


600 


.42 


.6 


864 


700 


.49 


.7 


1008 


800 


.56 


• 8 


1152 


900 


.63 


• 9 


1296 


1000 


.7 


1. 


1440 


2000 


1.4 


2. 


2 880 


3000 


2.1 


3. 


4 320 


4000 


2.8 


4. 


5 760 


5000 


3.5 


5. 


7200 


6000 


4.2 


6. 


8 640 


7000 


4.9 


7. 


10 080 


8000 


5.6 


8. 


11 520 


9000 


6.3 


9. 


12 960 


10 000 


6.9 


10 


14 400 


25 000 


17.4 


25 


36 000 


50 000 


34.8 


50 


72 000 


75 000 


52.2 


75 


108 000 


100 000 


69.5 


100 


144 000 


200 000 


138.9 


200 


288 000 


300 000 


208.3 


300 


432 000 


400 000 


277.8 


400 


576 000 


500 000 


347.2 


500 


720 000 


600 000 


416.7 


600 


864 000 


700 000 


486.1 


700 


1008 000 


800 000 


555.6 


800 


1152 000 


900 000 


625.0 


900 


1296 000 


1000 000 


694.5 


1000 


1440 000 


2000 000 


1388.9 


2000 


2 880 000 


3000 000 


2083.3 


3000 


4 320 000 


4 000 000 


2777.8 


4000 


5 760 000 


5000 000 


4372.2 


.5000 


7 200 000 


6000 000 


4166.7 


6000 


8 640 000 


7000 000 


4861.1 


7000 


10 080 000 


8000 000 


55.55.6 


8000 


11 520 000 


9000 000 


6250.0 


9000 


12 960 000 


10 000 000 


6944.5 


10000 


14 400 000 



This table will be most convenient in making quick com- 
parisons as between different wells in Dakota and those 
elsewhere where, as a rule, the flow is reported as so much 
per day while in Dakota the flow is always so much per min- 
ute. The greatest wells outside of Dakota are those of Kern 
Co., California, which flow from 150,000 to 4,000,000 gallons 
per day or (see table) from 104.3 (69.5 + 34.8) to 2,777.8 gallons 
per minute. Of their 54 wells only 10 flow over 1,200,000 gal- 
lons per day or 833 4 gallons per minute. This table shows 
at a glance the superiority of the Dakota wells. 

Example of use of table. How many gallons per minute 
flow from a well throwing 5,359,800 gals, per day ?— Add the 
quantities in 2d. column 3,472.2 + 208.3 + 34.8 + 6.3+ .56 
= 3,722.16 gallons per minute. 



84 



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85 

By interpolation other quantities may be readily taken 
from the foregoing table ; thus — 

To cover 10 acres S}4 inches deep, 

Multiply 36,300 (amount for 1 inch) by 8 = 290,400 

and add M of 36,300 " " " '' = 18,150 

Total = 308,550 cu. ft. 

Where the required acres and the required depth are 
neither one in the table as— Required the cu. ft. to cover 17 • 
acres 7 inches, — proceed thus— 

Take out quantity for 1 acre and multiply by the given 
number of acres. 

Thus — To cover 1 acre 6 inches = 21,780 

" 1 " 1 inch = 3,630 

" . " 1 " 7 inches = 25,410 

25,410 X 17, the given number of acres = 431,970 cubic feet, 
OR if the inches cannot be taken from the table as in above 
case multiply the amount for one inch by the given number 
of inches. Thus, amount for 11 inches = 3630 (amount for 
one inch) X 11 = 39,930 cu. ft. 

The volume in gallons may be found by multiplying the 
total cu. ft. by 7.48052, the number of gallons in one cu. ft. 

0?' 

by interpolation from Section B. How many gallons in 
308,550 cu. ft. (amount to cover 10 acres 8^ inches deep) ? 
From Section B. we find 3,258,500 as gals, to cover 10 acres 1 
foot or 24 half inches; 83^ inches = 17 half inches, therefore, 
divide 3,258,500 by 24, to get amount for one half inch, and 
multiply this quotient by 17 to get gals, for 17 half inches. 

OR see table No. :B6 

The time required for a well of given volume per minute 
to throw any given quantity of water is found by dividing 
the total volume by the volume of the well per mmute and 
then reduce the number of minutes thus found to hours, 
days, weeks, &c . or 

If the quantity is given in the foregoing table take out the 
time from Section C. or, if the quantity is not given in the 
table proceed as in the following. Example: 9 inches deep 
on 100 acres from a 500 gal. well will take— 

2,178,000 cu. ft. = 6 inches. ) sj^„>„ I 32,585,000 = gals, on 100 Ac. 1 ft. deep 
1,089.000 " " = 3 -' [ ^^^ ^ (Sec. B.) divided by 12 = 2.715,417 X 9 
3,267,000 cu. ft. = 9 inches. > ^ ' i= 24,438,753 = gals, at 9 inches. 

From Section C we find it takes a 500 gal. well 1 mo., 15 ds., 6 hrs., to 
cover 100 acres 12 inches deep, or 1,086 hours. Since 9 = % oi 12 take ^ of 
1,086 hours = 813 hours or 33 days and 21 hours. Ans. 

From table 35 (next page) an approximation may be quickly taken. 
Thus, Tinder head of 500 gal. well we see 21.600,000 = gals, thrown in 1 mo. 
and 720,000 = gals, in 1 day. 720,000 X 4 = 2,880,000 gals, which added to 
21,600,000 gals. = 24,480,000 gals, in 34 days, or a little more than our esti- 
mated amount of 24,438,753 gals. From this it is shown that the amount 
will be thrown in a little less than 34 days (33 ds. 21 hours as above.) 

For exact amounts and times one should figure exacfly which may be 
done from the tables by using a few more figures. 



86 



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87 



TABLE NO. 36. 

TABLE SHOWING EQUIVALENCE OF CUBIC FEET 
AND GALLONS— AND GALLONS AND 

CUBIC FEET. Neto. 



Cubic feet to gallons. 


Gallons to cubic feet. 


Cubic feet. = 


1 
= Gallons. 


Gallons. = 


Cubic feet. 


1 


7.48 


1 


.133679 


2 


14.96 


2 


.267358 


3 


22.44 


3 


.401037 


4 


29.92 


4 


.534716 


5 


37.40 


5 


.668395 


6 


44.88 


6 


.802074 


7 


52.36 


7 


.935753 


8 


59.84 


8 


1.069432 


9 


67.32 


9 


1.203111 


10 


74.80 


10 


1.336790 


20 


149.61 


20 


2.673580 


30 


224.41 


30 


4.010370 


40 


299.22 


40 


5.347160 


50 


374.02 


50 


6.683950 


60 


448.83 


60 


8.020740 


70 


523.63 


70 


9.357530 


80 


598.44 


80 


10.694320 


90 


673.24 


90 


12.031110 


100 


748.05 


100 


* 13.367 


200 


* 1496 


200 


26.735 


300 


2 244 


300 


40.103 


400 


2 992 


400 


53.471 


500 


3 740 


500 


66.839 


600 


4 488 


600 


80.207 


700 


5 236 


700 


93.575 


800 


5 984 


800 


106.943 


900 


6 732 


900 


120.311 


1000 


7 480 


1000 


* 133 


2000 


14 961 


2000 


267 


3000 


22 441 


3000 


401 


4000 


29 922 


4000 


534 


5000 


37 402 


5000 


668 


6000 


44 883 


6000 


802 


7000 


52 363 


7000 


935 


8 000 


59 844 


8000 


1069 


9000 


67 324 


9000 


1203 


10 000 


74 805 


10 000 


1336 


100 000 


748 052 


100 000 


13 367 


1000 000 


7 480 520 


1000 000 


133 679 


10 000 000 


74 805 200 


10 000 000 


1336 790 


100 000 000 748 052 000 | 


100 000 000 


13 367 900 



Note change in location of decimal point at*** 
This table will be of great use in quickly converting cubic feet to gal- 
lons or vice versa. 
Example, How many gallons in a reservoir containing 6,450,620 cu. ft.? 
Takefrom the table the gallons for 1,000,000 cu. ft. and X it by 6, also 
the gallons for 100,000 cu. ft. and X it by 4, &c., as shown below. 

= gals for 6 000 000 cu ft 
= " " 400 000 " " 
= " " 50 000 " " 
= " '• 600 " " 

= " " 20 " " 



7,480,520 X 6 = 44,883,120. 

748,052 X 4 = 2,992,208. 

74.805 X 5 = 374,025. 

600 = 4.488. 

20 = 149.61 . 



Total yards = 48,253,990.61 . = 



6 450 620 



OR 

Multiply the total 
cubic feet b y 
7.48052 , the gallons 
in one cubic foot 
This requires, 
more figures. 



88 

TABLE NO. 37. 

Table showing volume in gallons and in cubic feet thrown by wells 
of different volumes per minute, in periods of one month (30 days) 
and three months (90 days). New. 



ONE MONTH. 1 


THREE MONTHS. 


Gallons per 
MINUTE 

thrown by 
well. 


Total gallons 

thrown in 

1 month. 

(30 ds.) 


Equivalent 
volume in 
ucbic feet. 


Total gallons 

throwai in 

3 months. 

(90 ds.) 


Equivalent 
volume in 
cubic feet. 


1 


43 200 


5 775 


129 600 


17 325 





216 000 


28 873 


648 00 ) 


86 619 


10 


432 000 


57 748 


1 296 000 


173 244 


20 


864 000 


115 497 


2 592 000 


•346 491 


25 


1 080 000 


144 .373 


3 240 000 


433 119 


30 


1 296 000 


173 247 


3 888 000 


519 741 


40 i 


1 728 000 


230 996 


5 184 000 


692 988 


50 i 


2 160 000 


288 745 


6 480 000 


866 235 


60 


2 592 000 


346 495 


7 776 000 


1 039 485 


70 


3 024 000 


404 244 


9 072 000 


1 212 732 


80 


3 456 000 


461 993 


10 868 000 


1 385 979 


90 


3 888 000 


519 743 


11 664 000 


1 559 229 


100 


4 320 000 


577 492 


12 960 000 


1 732 476 


200 


8 640 000 


1 154 986 


25 920 000 


3 464 958 


300 


12 960 000 


1 732 479 


38 880 000 


5 197 437 


400 


17 280 000 


2 309 972 


51 840 000 


6 929 916 • 


500 


21 600 000 


2 887 466 


64 800 000 


8 662 398 


600 


25 920 000 


3 464 959 


77 760 000 


10 394 877 


700 


30 240 000 


4 042 452 


90 720 000 


12 127 356 


800 


34 560 000 


4 619 945 


103 680 000 


13 859 835 


900 


38 880 000 


5 197 439 


116 640 000 


15 592 317 


1000 


43 200 000 


5 774 932 


129 600 000 


17 324 796 


1100 


47 520 000 


6 .352 425 


142 560 000 


19 057 275 


1200 


51 840 000 


6 929 919 


1.55 5-.'0 000 


20 789 757 


1300 


56 160 000 


7 507 411 


168 480 000 


22 .522 2.33 


1400 


60 480 000 


8 084 905 


181 440 000 


24 254 715 


1500 


64 800 000 


8 662 399 


194 400 000 


25 987 197 


1600 


69 120 000 


9 239 891 


207 360 000 


27 719 673 


1700 


73 440 000 


9 817 385 


220 320 000 


29 452 155 


1800 


77 760 000 


10 394 878 


233 280 000 


31 184 634 


1900 


82 080 000 


10 972 372 


246 240 000 


.32 917 116 


2000 


86 400 000 


11 549 865 


259 200 000 


34 649 595 


2100 


90 720 000 


12 127 358 


272 160 000 


36 382 074 


8200 


95 040 000 


12 704 852 


285 120 00'.) 


38 114 556 


2 300 


99 360 000 


13 282 344 


298 080 000 


39 847 032 


2400 


103 680 000 


13 859 838 


311 040 000 


41 579 514 


2 500 


108 000 000 


14 437 332 


324 000 000 


43 311 996 


3000 


129 600 000 


17 324 798 


388 800 000 


51 974 394 


3 500 


151 200 000 


20 212 264 


453 600 000 


60 636 792 


4 000 


172 800 000 


23 099 731 


518 400 000 


69 299 193 


4 500 


194 400 000 


25 987 197 


583 200 000 


77 961 591 


5000 


216 000 000 


28 874 664 


648 000 000 


86 623 992 


5500 


237 600 000 


31 762 130 


712 800 000 


95 286 390 


6000 


259 200 000 


34 649 596 


777 600 000 


103 948 788 


7000 


302 400 000 


40 424 529 


907 200 000 


121 273 587 


8 000 


345 600 000 


46 199 562 


1 036 800 000 


138 598 686 


9000 


388 800 000 


51 974 395 


1 166 400 000 


155 923 185 


10 000 


432 000 000 


57 749 328 


1 296 000 000 


173 247 984 



See explanation on opposite page, 



89 

The table on opposite page is an extension of table on page 
86, but changed to give two periods or" time and wells of a 
greater range of volume per minute; and giving the volumes 
in both gallons and cubic feet. The irrigation season lasts 
about three months and is preceded in the spring and fol- 
lowed in the f 11 by about equal periods of time, so that one 
month and three months are the periods assumed to be 
those upon which the greater number will desire to base 
estimates as to the volumes they can count on during these 
periods. By simple addition the volume of any well may be 
taken from the table. 

Example — What volume will a well with a volume of 3572 gals, per min- 
ute throw in 3 months? 

3000 gal. well = 388,800,000 gals,— 51,974,394 cu. ft. 
500 '^ '• = 64,800,000 " — 8,662,398 
70 " " = 9,072.000 " — 1,212,732 
2 " " = 259,200 " — 34,650 



3572 " " 462,931,200 61,884,174 

Having the amount for 3 months, the amount for any 
lesser or greater time may be found by division or addition. 
Thus: In above example the well, in 40 days, would throw 
i-|-^=(30 ds.+iO ds.) of the total amount or volume shown; 
or in i}4, months a well would throw, total -j-i-j-i =(3 Mo.-f-l 
Mo -\-)4. Mo) of the total volume shown. 

The table will be found useful for taking out rapid approximations aa 
to volumes and in this will answer the purpose of the proceeding table — 
table 37— thus, by inspection it is shown that a reservoir holding about 
36,000,000 cu. ft. holds about 212, 000,000 gals, and that a 2100 gal. weU would 
be required in order to fill it in about 3 months. 



TABLE NO. 38. 

DISCHARGE OF .JETS IN GALLONS PER MINUTE. 



Head on 


Head on 


Discharge from .Jets of following diameters. 


Jet 
in Pounds. 


Jet 
in feet. 












K 


1 inch. 


1% 


m 


m 


' 1^2 


20 


46.16 


70.4 


125.2 


158 


196 


237 


282 


25 


57.70 


, 78.7 


140.0 


177 


219 


265 


315 


30 


69.24 


86.3 


153.4 


194 


240 


290 


345 


40 


92.32 


99.6 


177.1 


224 


277 


335 


398 


50 


115.40 


111.4 


198.0 


251 


309 


374 


445 


60 


1.38.48 


121.9 


216.8 


274 


339 


410 


488 


70 


161.56 


131.8 


234.3 


297 


366 


443 


527 


80 


184.64 


140.8 


250.3 


317 


391 


473 


563 


90 


207.72 


149.4 


265.6 


336 


415 


.502 


598 


100 


230.80 


157.5 


280.0 


354 


437 


529 


630 


110 


253.88 




293.6 


372 


459 


555 


661 


120 


276.96 




306.7 


388 


479 


580 


690 


1:30 


300.04 





319.2 


404 


499 


604 


718 


140 


323.12 





3.31.2 


419 


518 


626 


745 


1.50 


;346.20 
369.28 
392. :36 
415.44 






434 

448 


536 
553 
570 


649 
670 
690 
710 


772 


160 






797 


170 






823 


180 









845 



This table is calculated from the formula given on page 73 except that 
H. (head) in feet is taken at 2.308 ft. per pound of head instead of 2.311 as 
given. The difference is not material. 



90 



WIND MILLS. 

The following tables are from a circular issued by the Q. 
S. Department of Agriculture, office of Irrigation Inquiry. 

TABLE NO. 39. 

SIZE AND CAPACITY OF WIND MILLS AT VARIOUS DEPTHS. 



Diameter 


25 ft. Eelevation. 


50 ft. Elevation. 


100 ft. Elevation. 


of wheel 
in feet 


Size of 
pump in in. 


Gallons 
per hour. 


Size of 
pump, ins. 


Gallons 
per hour. 

300 

500 

800 

1200 


Size of 
pumpjins 


Gallons 
per hour. 


10 
12 
14 

16 


3% , 

i 

5 
6 


500 

750 

1150 

1500 


3 

31/3 

4 

5 


2% 
3 

31/2 
4 


200 
350 
550 

800 



This table is only intended as a general guide and is subject to modifi- 
cation by reason of some mills having greater capacity, for given size, 
than other mills ; and the same applies to the pump used and the manner 
of attachment. 

TABLE NO. 40. 

VOLUME OF WATEE PUMPED PER MINUTE. 

From 10 to 100 Feet. 



Diameter 

of 

wheel 


Vertical distance from water to point of delivery, in feet. 


10 


15 


25 


50 


75 


100 


Feet 


Gallons 


Gallons 


Gallons 


Gallons 


Gallons 


Gallons 


8.5 


15.24 

48.26 


10.16 
32.18 


6.16 

19.18 


3.02 
9.56 






10 


6.64 


4.25 


12 


86.71 


57.81 


33.94 


17.95 


11.85 


8.49 


14 


111.67 


74.44 


45.14 


22.57 


15.30 


11.25 


16 


155.98 


103.99 


64.60 


31.65 


19.54 


16.15 


18 


249.93 


159.95 


97.68 


52.17 


32.51 


24.42 


20 


309.60 


206.40 


124.95 


63.75 


40.80 


31.25 


25 


532.52 


355.01 


212.38 


106.96 


71.60 


49.73 


30 


1080.11 


728.83 


430.85 


216.17 


146.61 


107.71 



VELOCITY OF WIND. 

The average over the U. S., as determined by signal service examina- 
tions, is 5769 miles per month, or about 8 miles per hour. See page 91 — 
table of wind velocity in Dakota . Experience has demonstrated that to 
operate a wind mill, there is required an average velocity of wind of 6 
miles per hour. 







TABLE NO. 41 


. 




VELOCITY AND FORCE OF WIND.— ^asweiZ. 


Miles 


Feet 


Pressure 






per 


per 


per sq. ft. 


Description 




hour. 


minute. 


inlbs. 


of the wind. 


The mean weight of the 










• lto3 


88—264 


.005— .045 


Just perceptible 


air will support a column 


6 


440 


.125 


Pleasant wind 


of water 33.95 ft. high, at 


10 


880 


.5 


Fresh breeze 


sea level. The velocity of 


20 


1760 


2. 


Stiff breeze 


sound in air at 60° = 1107 


30 


2640 


4.5 


High wind 


ft. ,in water about 49,000 


45 


3960 


10.125 


Gale 


ft. per second. 


60 


5280 


18. 


Great storm 




80 


7040 


32. 


Hurricane 




100 


8800 


50. 


Tornado 





91 

TABLE NO. 42. 

WIND IN DAKOTA, 

Average daily and hourly Wind Velocity for 9 years from 1882 
to 1891J inclusive, at Huron, S. D., by Sam. W. Glenn, U. S. 
Weather Bureau. 



Month. 


Average daily 


Average hourly 


velocity, miles. 


velocity, miles. 


January 


332.5 


9.7 


February 


242.6 


10.1 


March 


239.9 


10. 


April 


274.8 


13.1 


May 


265.7 


11.1 


June 


238.6 


9.9 


July 


220.2 


9.2 


August 


217.5 


9.0 


September 


254.0 


10.6 


October 


244.7 


10.0 


November 


227.0 


9.5 


December 


224.2 


9.3 



Average hourly velocity for 9 years = 10.1 miles. 
TABLE NO. 43. 
EAIN IN DAKOTA. 

Total Rain Fall bj' months as recorded at Huron, S. D., from 1881 to 1892 
by S. W. Glenn, Jj . S. Weather Bureau. 



Year. 


.Jan FebjMch Apr. 


May 


June 


July 


Aug. j Sep. 


Oct. 


Nov. 


Dec. 


Tot'l 


ISSl 


. .! . 










3.. 58' 6.31! 3.11 
5.8S' 1.44; .86 


2.10 
3.37 


.45 
.61 


.06 
.23 




1882 


.14| .25 


.80 


4.18 


4.50 


5.86 


28,12 


1883 


.171 .47 


.42 


2.14 


4.45 


4.33 


o.20| 1.77 1.68 


1.96 


.05 


.61 


23.25 


1884 


.09 .58 1.53 


2.70 


2.90 


3.18 


5.111 1.18 1.26 


1.52 


.17 


.62 


20.84 


1885 


.15 .22 .12 1.06 


5.20 


5.43 


4.52 3.891 2.61 


.98 


1.50 


.10 


25.78 


1886 


.48 .16 .62 3.52 


1.58 


1.90 


1.60 


5.62 1.59 


1.26 


1.18 


.74 


20.25 


1887 


.33:1.11 .64 3.72 


1.38 


3.9.-! 


4.96 


6.13 .15 


.79 


.25 


2.09 


25.54 


188^ 


.78' 


.52il.22 i .88 


4.98 


1.10 


3.11 


3.46 .19 


.29 


.34 


.18 


17.05 


1889 


1.26 


.93i .19 


3.41 


3.04 


1.04 


3.51 


.66 


3.89 


..55 


.16 


1.53 


20.17 


1890 


.66 


.18! .32 


.64 


2.88 


5.87 


1.41 .73 


.32 


.61 


.38 


.68 


14.68 


1891 


.07 


1.3211.64 

1 


3.45 


.44 


8.03 


1.01 1.43 


.47 


.78 


.94 


.54 


20.17 


Mean 


.41 


.57i .72 


2.57 


3.14 


4.03 


3.63 2.96| 1.46 


1.29 


.55 


.67 


21.58 



1892 I .28 I .70 I 1.11 i 5.90 | 6.03 | 4.00 I Total in 6 months=18.02 

Read carefully the note on the next page with reference to this table. 
Read it twice— and don't forget it. 

PRECIPITATION FOR FIRST 6 MONTHS 
DURING THE FOLLOWING YEARS. 



1 1882 1 15.73 


1886 


8.26 


1890 


10.55 


1883 1 11.98 


1887 


11.16 


1891 


15.00 


1884 10.98 


1888 


9.48 


1892 


18.02 


1885 12.08 


1889 


9.87 


lAv'g. 


12.10 



(See also table No. 14.) 



92 

Note— As to precipitation table No. 43. 

This table of rain-fall has much interest as it shows the 
distribution and amount of our rains by months and years. 

1882 was Dakota's "boom" year in rain-fall, as in other re- 
spects, and was the most bountiful on record in consequence. 
1883— '85 and '87 were good years, while 1888— '89 and '90 
were years of almost total failure. It will be of special in- 
terest to note that 1889 and 1891 have exactly the same total 
rain-fall; whereas 1889 was a year of drouth and failure, 
while 1891 was a year of phenominally good crops. Note 
further that the record of 1891 followed a record of but 14.68 
in 1890; whereas the equal record of 1889 followed a record of 
17.08 for 1838, so that, so far as the records for the two-year 
periods are concerned, the period of '89 and '90 ought to 
have shown better results than the period of '90 and 91. 

Note still further that the rain-fall of 1889 for the months 
from January to July was but 13.36 inches out of the total of 
20.17; whereas in 1891 the rain-fall for these months was 
16.01 out of the total of 20.17. Herein, then, lies the secret 
of the good year 1891- during the groioing months of 1891 
there was a rain fall of 2.65 inches greater than during these 
months of 1889— the totals for the two years being the same. 

In 1889 the rain came too late, while in 1891 it came in the 
proper season . 

A valuable lesson may therefore be drawn from the table 
— it is, that the 2 or 3 inches of timely rain in 1891 saved Da- 
kota from a fourth year of failure, and enriched the people 
at the rate of 

OYER $5,000,000 PER INCH. 

There is the record! There is the lesson! 

From this draw the further lesson as to the true value of 
the water of a well the distribution of which you have in 
your absolute control both as to the quantity and the time 
when it shall be used. 

If this lesson alone is well learned by a few then will that 
one table have made this little book well worth the cost of 
publishing. 



Year 


First 
Frost 


Last 
Frost 


Temperature. 






Days 




Highest 


Lowest 


Clear. 


Fair 


Cloudy 


Rain 


*1881 


Sept 15 




95.6° 


— 6° 


62 


81 


41 


66 


1882 


" 20 


May 22 


93.7 


—20 


113 


171 


81 


96 


1883 


July 17 


April 30 


99.2 


-32 


110 


168 


87 


11.5 


1884 


Sept 11 


May 13 


95.9 


—38 


139 


155 


72 


111 


1885 


" 1 


June 8 


98.2 


-33 


129 


164 


72 


95 


1886 


Aug. 31 


May 6 


103.6 


-33 


121 


180 


64 


118 


1887 


Sept. 15 


" 3 


99.2 


—43 


130 


162 


73 


114 


1888 


" 12 


•' 18 


101.7 


—36 


141 


142 


83 


95 


1889 


" 5 


" 2 


104.0 


-30 


133 


143 


89 


92 


189() 


Aug. 22 


" 15 


103.0 


-28 


151 


150 


64 


90 


1891 


•' 23 


" 16 


97.0 


—24 


135 


136 


94 


92 



Records from Huron, S. D., Signal Station. 
*From July 1st 1881. 



93 

TO MEASURE THE HEIGHT OF A STREAM. 

The following method will enable any one to easily and 
quickly measure the exact height of the stream thrown out 
by a well, without the use or instruments or of tables of 
tangents. 

Referring to figure 11 let W be a well and EF the stream 
thrown, ('arefully measure otf a distance of say 100 feet 
and drive a stake S, to the level of the pipe if possible. 
Drive another 3 or 4 feet nearer and across the top nail a 
piece of board B ; which set level. Measure off AC = 5 feet 
(or any other amount) and nail the stick H to this mark, 
and at right angles to AC. Now look over the point of the 
board at A and have some one mark on the stick H a point 
D in line with E the top of the stream EF. Measure the 
length CD, then may the height EF be found by simple 
proportion. 

Example. AF = 100 ft. AC = 5 ft. CD = 4 ft. then, 

AC : AF : : CD : FE or 5 : 100 : : 4 : (required height) 

100 X 4 = 400, 400 ^ 5 = 80 ft. = height of stream EF. 

If the horizontal line AF will not strike the top of the 
pipe, as at Y, measure the distance YZ and subtract it from 
the total height found. 

Although a rough method it is an easy one and sufiicient 
accuracy may be obtained. If this is done by all wells, while 
throwing streams of different sizes, and a record made of 
the results it will be a vast improvement on the guess-work 
so freely indulged in heretofore. 

Fig. 11. 
Method of measuring height of a stream. 



^ 



y 



^ 



S' 



B 



y 






fOO 




(See also page 147.) 



94 




^|2 0"-3C 

M I RAIN '>-^ A^r^T^} 

HEFERENCE 

==1=10-15 in. rain 
^ I _ ^ ^ . 

CcmpUed % Professor G. S. Bailey. Jiapid City, Dakota 



Xongitude "West 



From Harper's Masaztne. 



Copyriglit, 1889, by Harper & Brothers. 



FIG, 12. WEATHER MAP OF NORTH AND SOUTH DAKOTA. 

By permission of Messrs. Harper & Brothers. 

Showing isothermal lines and areas of varying rainfall. It will be 
seen that nearly all of the agricultural section of both states has a 
range of rainfall of from 15 — 20 inches. This area should extend 
farther to the South than shown on the map. 



95 




From Harper's Magazine. — Copyriiiht, 1889, by Harper & Brothers. 



Fig. 13. View of Brick- Yard Well at Yankton, S. D. 

From photograph by L. Janousek, Yankton. 
By permission of Harper and Brothers. 

Depth = 595 feet. Size of pipe = 6 inclies. 

Pressure = 48 to .57 5)s. per square inch. 

Volurne = 1620 to 2000 gallons per minute. 

Location, on top of the Missouri river blufEs. 

Use, for power. Cost, about $8,000. 

The view as taken showed the well throwing a 6 inch stream about 6 feet 
above the top of a 20 foot stand-pipe. This well is one of a number of 
large wells in the southern portion of South Dakota having a compara- 
tively low pressure and very large volume. 



96 

RESERVOIRS. 

In the western states where irrigation by water taken from 
streams is the rule, and irrigation by well waters the excep- 
tion, the waters are, in most cases, impounded at some place 
near their head waters where the topography is such as to 
admit of the construction of a dam which will create a res- 
ervoir in the valley wherein are stored the waters of the 
freshet season for use, many miles away, during the season 
of drouth. Such vast engineering works can only be entered 
upon by corporations possessing vast capital, for, in some 
cases, the dam, with flumes and ditches to convey the water 
to the irrigated districts, has cost over a million dollars. 

The general government has already provided for the lo- 
cation, survey and reservation of all sites on the public do- 
main where dams and reservoirs may, to advantage, be lo- 
cated in the future, and wise restrictions have been thrown 
around corporations securing such sites so as the best to pro- 
tect the individual comsumers from corporate exactions 

Vast tracts of the tin est land in the world lie undeveloped 
and barren because the necessary capital has not yet been 
found to improve it by flrst constructing a dam and creat- 
ing a reservoir for the storage of the necessary water. 

IN DAKOTA how different is all this? 

There is not in the state a reservoir site worthy of the 
name and no money need be expended on great engineering 
works for the storage of water. Nor is there a stream that 
can, to advantage, be dammed. The Dakota reservoir will 
rarely if ever exceed 10 acres in area and in place of one cov- 
ering many miles there may be several small ones on one 
mile. 

When artesian irrigation was flrst agitated it was the 
popular belief that the well waters might be run directly 
into the ditches and thence distributed; but no thought was 
given to the fact that thereby the service of a well of but 
moderate volume would be very limited, for the water flow- 
ing within any given time would be insufficient, within that 
time, to cover any considerable area. 

If, however, the waters could be stored in a reservoir dur- 
ing such periods as it was unnecessary to apply any to the 
land then when water was needed over a broad area, and 
within a brief period of time, the accumulated store could be 
made to do service which the well alone could not do in the 
same time. The necessity for small storage reservoirs being 
thus apparent they become as much a part of every irriga- 
tion plant as the well itself. In fact if the land under ser- 
vice of any particular well is quite rolling it may, and in 
many cases will, be necessary to have two or more small res- 
ervoirs on the farm in order to secure the best service to the 
land and the most economical storage and distribution. 

Reservoirs being necessary, how and where shall thev be 
built? 



97 
LOCATION. 

The highest points will, of course, be the natural sites for 
reservoirs but the land may lay so as to make it not only 
better but cheaper not to locate tlje reservoir on the highest 
point. Such cases will be few and the conditions in mind 
will in all such cases be apparent to one on the ground. If 
a tract of land is divided into two or more parts by a gully 
or depression of any extent it may be best in such case to 
have two or three smaller reservoirs, one on each tract or 
division of the land. If but one large reservoir were built 
the other tracts or elevations would have to be served from 
flumes which would be larger and more expensive than one 
sufficient to feed the reservoir alone, and they might, at the 
critical time, fail to do proper service by reason of adverse 
winds or other causes thereby causing more loss than a 
reservoir would cost. 

In ordinary cases the proper site for a reservoir may be se- 
lected by a farmer without the aid of an engineer but where 
any doubt exists as to the choice of locations then no chances 
should be taken and the services of one competent to judge 
should be secured. 

FORM. 

In most cases the circular form will be adopted because 
the greatest area is enclosed by a given amount of bank. 
Occasional departures from this form will be necessary by 
reason of the lay of the land. 

Only the cicular form will be considered in the tables. 
SIZE. 

The matter of size will, in a few cases, be governed by the 
land but, as a rule, the service to be rendered by the waters 
stored will govern. If a township well is to be provided 
with storage then the volume of the well should be deter- 
mined in order to know how small a reservoir would suffice 
not only to give service to the area to be irrigated but also 
to hold all the water the well will supply within the longest 
time it could be permitted to run without allowing the wa- 
ter in the reservoir to be drawn off. This would give all the 
necessary storage capacity without any waste of money in 
making it larger than needed. 

Since most wells throw over 500 gallons per minute the 
time of impounding could not be long except with a very 
large reservoir. Table No. 37 taken in connection with ta- 
bles 47 and 48 will quickly supply all needed information in 
this connection. From them it will be seen that a 500 gallon 
well will fill a 10-acre reservoir seven feet deep every .30 days, 
&c., &c. Where, as in case of a township well which will be 
used to serve several farmers, the volume used will be large 
the storage capacity should be as large as economy will war- 
rant and each consumer might to his own advantage be sup- 
plied with a sub-reservoir. In case of special-service or sub- 
reservoirs which are designed to serve only a limited area as 
for example, a knoll of 10 or 15 acres then the water to be 



98 

used on that area alone should be estimated and storage area 
provided only sufficient for that volume, allowance being 
made for seepage, evaporation and waste. Thus, assume a 
field of 10 acres to be supplied by a sub-reservoir and volume 
sufficient provided to flood the land 6 inches; what would be 
the size of reservoir required if the water be given a depth 
of 5 feet in the reservoir ? Table 34 or table 21 gives the cu- 
bic feet of water required to flood 10 acres 6 inches deep as 
217,800. Table 29, under head of water 5 feet deep, shows at 
a glance that a reservoir of 13^ acres will hold this volume 
and enough more to cover all waste. Table 45 gives the 
diameter, circumference and area of this reservoir. 

These suggestions will show the importance of duly con- 
sidering the elements of volume of well, time it may flow, 
area to be served, &c., in the laying out of a reservoir for 
either general or special service. The depth of water in the 
reservoir will always enter into the consideration. 

Where any considerable volume is required it will be best 
to have the depth in excess of 4 feet, first, because if the wa- 
ter is deeper the reservoir will occupy less ground for a given 
capacity ; second, the evaporation will be less, the exposed 
area being less, and the waste from seepage will be less; 
third, the wash of the banks will be less because the wind 
will have less sweep over the surface. 

Table of sizes. 

Table No. 45 shows the diameters, circumferences, and 
areas in sq. ft. of reservoirs from % acre to 10 acres, for 
each ^ acre, and explanation follows as to calculating the 
elements for othe r sizes. 

LAYING OUT. 

The size having been determined the staking out follows. 
If the reservoir is to cover a given area the whole bank will 
be within that area and the foot of the outer slope will 
bound the given area. If the area is to exclude the bank the 
foot of the inner slope will bound the area. If the water is 
to cover a given area then the high water line or the point 
half way down the bank therefrom will bound the given area. 
Or the area may be bounded by the center line either of the 
whole bank or of the top of the bank. 

Usually these considerations will not be of much import- 
ance, but in case of joint ownership or of contracting for 
the construction they may be important and should then be 
clearly understood and carefully specifled . In staking out 
it will be best, for the convenience ot graders, to drive stakes 
on the outer and inner lines of the bank. The line of the 
top follows as a result of the slopes. 

The measurement may be made with a measured wire 
one end of which is fastened or held at the center while the 
outer end is carried around and stakes driven at convenient 
distances along the circle. If wire cannot be had then rope 
or even binding twine will answer the purpose. 



99 

If the land is uneven or covered with stubble, corn stalks, 
growing grain or other obstructions which prevent swing- 
ing the wire or line around the center point then two per- 
sons may manage the wire or line as follows. — A holds one 
end at the center while B drives stakes at the north points; 

{At both the inner and outer slopes of the banks.) 

both then walk south across the circle until B reaches the 
center when A drives the south stakes; they then walk back, 
B turning a little to the east or west, until A comes again 
to the center while B drives stakes at the outer end; A 
then, as before, walks straight across the circle and drives 
other stakes. Repeat this until the circuit of the circle has 
been made and all the stakes set . The result is the same 
but the walking a little more. Any farmer can thus lay 
out his own reservoir, if need be, in an hour's time and do 
it as well as it could be done by an engineer at an expense 
to the farmer of $5 to $10. The outlines having been staked 
out, and the stakes numbered, the levels should be taken to 
determine the height of the bank at each stake. If the 
ground is not fairly level the stakes will have to be set in 
or out to give the proper base line according to the length 
of the slope. 

Where the ground is comparatively level any farmer can 
do his own leveling not only for reservoirs but for ditches, 
but where it is rolling the services of an engineer should be 
secured as a measure of economy. Better to pay for having 
the work properly done by responsible parties than to do it 
wrong and then be obliged to have it done over again. 

See notes on leveling, page 128 and following pages. 

THE BANKS. 

The banks should be constructed of as firm earth as pos- 
sible in order to give strength and prevent percolation and 
washing, and they should be thrown up by drag scrapers 
which results in a more solid and firmly packed bank than 
can be made by the use of wheel scrapers or graders unless 
the work with the latter be properly done. (See embank- 
ments and footings— under head of Ditches.) The outer 
slope may be one of 13^ horizontal to 1 vertical. The 
breadth of the top will depend upon the height and strength 
required. Most reservoirs will be 9 feet or less in height 
and for such heights a width of top of 5 feet will be suffic- 
ient. Where the bank exceeds 9 feet in height an additional 
foot in width may be added for each 2 feet of additional 
height, the slopes remaining the same. 

Fig. 14, on the next page shows in sectional diagram the inner slopes of 
banks from 1 ft. to 14 ft. high and with slopes of 2 to 1. The horizontal 
lines indicate the water levels and the diagonal lines the slopes of the 
banks. The upper horizontal line of figures indicate the distances of the 
foot of the banks from the top (measured horizontally ;) and the lower 
line of figures the amount the diameter of the reservoir is reduced by 
banks of the different heights. Thus, if the bank is 8 feet high and the 
water 4 ft. deep the shore line will be at A and the area of the water sur- 
face will have a diameter 21 feet less than that of the reservoir (measured 



100 

to center line of top.) To get the volume, take the diameter half way 
down the bank, at C, which is 29 ft. less than the total diameter, and pro- 
ceed as explained in the tables. The further use of the diagram will be 
apparent. Similar diagrams may easily be constructed for use with other 
slopes or for banks of greater height than here given. 

As to construction of footings for banks see remarks under head of 
Ditches, on page 119, and as to cost of grading, &c., see "Excavation and 
Cost," P. 117. Fig. 14. 

Slope Diagram for Banks of Reservoirs. 




te 



/6 £0 22 



4^ e Q to IS /4 
FE£T TO FOOT OF BANK . 

9 13 I? ai 25 29 33 S? 41 45 49 
OfAA^ET£R Of ff£S. TO BE BBDUCED fiV— fT. 



Table No. 44 shows the cross sections of banks from 3 ft. to 10 ft. high ! 
with area of cross Sections and cubic yards of earth per lineal foot and 
per 100 feet. 

This table will be of use to contractors and graders. 

To find the cubic contents of a bank X the area of the cross section by 
the length of the bank in feet and then divide by 27. Thus, in first exam- 
ple given in the table, the area of the cross section = 6 X 10 = 60 ) Total 

20 X 5 = 100 ^ = 235 
15 X 5 = 75)sq. ft. 
this X 1656 (the circumference of a 6 acre reservoir) = 389,160 cubic feet 
which -4- 27 = 14,413 cu. yds. ; by table— 870.37. the cu. yds. in 100 ft- X 16.56 
= 14.413 the same as by the other and longer method. 

WASHING OF BANKS. 

. The washing down of the banks by the waves in the reservoir is a mat- 
ter of much importance and yet little can be said as to the best means of 
preventing it. Where, as is the case in some sections, there are plenty of 
stone the water line may be partially protected by riprapping with them 
but this involves a large amount of labor. In most sections of the state 
there are no stone so other means must be used. In sections near the 
James, or other rivers, along which willows grow these willows may, at 
but little expense, be transplanted in the banks where they will form a self 
maintaining protection. Nor can this expedient be practiced by but few. 
The tough prairie sods taken from the surface of the ditch may be laid 
aside and be afterward laid along the water line. This has been tried and 
has worked well and, although much labor is involved it probably re- 
mains the best for general use. Where gravel may be had a shore line may 
be covered with it thus forming a natural water break. In some cases it 
may be best to construct a break-water of plank sharpened and d^'iven into 
the bank or laid to posts set in the bank. The steeper the bank the great- 
er of course will be the displacement of the earth by wave action. 
Outlets and Gates— See P. 107. 



101 



TABLE NO. 44. CROSS SECTIONS OF RESERVOIR BANKS 
WITH AREAS AND CUBIC CONTENTS. New. 



,„^ o SEC^TIONS 


Area of 
cross 

section 
Sq. ft. 


Cu Yds 

perf t of 

bank 


Cu. Yds. 
per 100 ft. 
of bank. 


2.35 

189. 

iri2. 


8.7037 


870.37 


roTAt IV / or « 41* 






7.0 
5.6296 






700.0 


^7* 








..-''^^^ /6* 1 /2' \. 


.562.96 


33' 




.. . ,., ... 


122.5 


4.5370 




^^ 14.' I //' ^V 


453.70 


BO' 






93. 


3.4444 






344.44 


«€• 






70. 


2.5925 




^-^ 10' 1 1 a* \ 


259.25 


a3' 






48. 


1.7777 






177.77 


/9' 




^'^^ j'^ : 5^ 


31.5 


1.1666 


116.66 


/«• 






44. 


1.6296 




.--<TT>\ 


162.96 


/fl- 




•*■ 


28.5 


1.0505 




.^--^i^ iJ^ 


105.05 


/s- 






102 



TABLE NO. 45. RESEEVOIR TABLE. 
Diameters, Circumferences and Areas in square ft. of reser- 
voirs from % acre to 10 acres in area — advancing by 3^ acre. 

Neu\ 



Area in 


Diameter 


Circmuference 


Area in Square 


Acres. 


in feet. 


in feet. 


feet. 


Vs 


83+ 


261 


5 455 


M 


118— 


371 


10 890 


H 


167— 


525 


21780 


% 


204— 


641 


32 670 


1 


235— 


738 


43 560 


M 


263+ 


826 


54 450 


M 


288+ 


905 


65 340 


% 


312— 


980 


76 230 


2 


333+ 


1046 


87120 


M 


353+ 


1109 


98 010 


% 


372+ 


1169 


108 900 . 


M 


391— 


1228 


119 790 


3 


408— 


1282 


130 680 


M 


425— 


. 1335 


141 570 


% 


441— 


1385 


152 460 


M 


456+ 


1433 


163 350 


4 


471+ 


1480 


174 240 


M 


486— 


1527 


185 130 


5 


500— 


1571 


196 020 


M 


513+ 


1612 


206 910 


5 


527— 


1656 


217 800 


M 


540— 


1696 


228 690 


% 


552+ 


1734 


239 580 


M 


565— 


1775 


250 470 


6 


577— 


1813 


261 360 


M 


589— 


1850 


272 250 


y% 


601— 


1888 


283 140 


M 


612— 


1923 


294 030 


7 


623+ 


1957 


304 920 


M 


634+ 


1992 


315 810 


y% 


645— 


2026 


326 700 


M 


656— 


2061 


337 590 


8 


666+ 


2092 


348 480 


M 


676+ 


2124 


359 370 


y% 


687— 


2158 


370 260 


% 


697— 


2189 


381 150 


9 


707— 


2221 


392 040 


M 


716+ 


2249 


402 930 


M- 


726— 


2281 


413 820 


M 


735+ 


2309 


424 710 


10 


745— 


2340 


435 600 



Note — In the above table the diameters and circumferences are taken to 
the nearest foot. The area in square feet is correct for the given areas in 
acres. The signs of + and — after the diameters indicate whether the di- 
ameters given are too large or too small. Thus, 83 + indicates that a 
fraction of a foot, less than Vz , must be added to 83 to give the true diam- 
eter ; and 118 — indicates that a fraction less than H foot must be taken 
from 118 to give the true diameter ; 83 is therefore a little too smaU and 
118 a little too large— less than Vz foot in each case. See explanation on 
next page. 



103 

Explanation as to table 45. Table No. 45 is constructed 
from table 72; the areas in square feet having first been cal- 
culated. The area in sq. ft. of a 5 acre res. being 217,800 
enter table 72 in the column of areas and find 2181.28 as the 
area of a circle whose diameter is 52.7 and circumference 
165.56. This tabular area agrees most nearly with the given 
area in sq. ft. 

Therefore, for a circle of 527 ft. diam. the circumference 
would be 1655.6 ft. {decimal point ONE place to the right.) 
and the area 2.1%, V2.^.{decimal point TWOplacesto the right.) 
This area corresponds most nearly to the given area and 
'hence the diameter and circumference are the ones most 
nearly corresponding to the given area. If diameter is less 
than 100 the area and circumf . may be taken directly from 
the table. If diameter is more than 100 and less than 1000 
enter the table 72 and from the first column take the whole 
number and decimal corresponding to the given diameter; 
then, for the area, move the decimal point TWO places, and 
for the circumference ONE place, to the right. Example, 
required the circumference and area of a circle or reservoir 
having a diameter of 472 ft. ? In table 72 opposite 47.2 (473) 
find circumf. = 1482.8 and area = 174 974.1 [The decimal points 

having been moved as above described'^ The area m acreS iS fOUnd 

by dividing the area in sq. ft. by 43560. 

If either the diameter, circumf. or area in sq. ft. or acres 
be given all the other elements may thus be found from 
table 72. 

"' EVAPORATION AND FILTRATION. 

Evaporation is the greatest during warm or windy weath- 
er; greater in shallow than in deep water and greater in run- 
ning than in still water. The evaporation from a ditch or 
reservoir during June, July and Aug. will rarely exceed .8 
to .4 inch per day. During the remaining months the aver- 
age will be about. I inch making for the year from 3 to 5 
feet of loss by evaporation. To the loss by evaporation must 
be added the loss by seepage or filtration either into the 
earth or through the banks. The amount of seepage through 
the banks will depend not only upon the character of the 
soil of which they are made but also upon the solidity with 
which they have been thrown up. So with the seepage into 
the earth. If the soil is of soft loam, sand or gravel the per- 
centage of loss will be much greater than if the sub-soil is of 
clay or hard-pan. 

The loss from both evaporation and seepage from a properly construct- 
ed reservoir on average ground may be assumed to be about 1 inch per day 
after the reservoir has been in use for a season. The following table will ' 
show the approximate volume of loss per day in gallons from reservoirs of 
different areas. 



TABLE NO. 

Showing loss 



46. 



i n Reservoirs 
from Evaporation and Filtration. 

Approximate only. 



iArea 
acres 

j 1 

: 2 

i 3 
! 5 


Loss in 
Gallons. 

27100 

54300 

81400 

108600 

135700 


Area 
acres 


Loss in I 
Gallons. 


6 

7 

8 

9 

10 


162000 
190000 
217000 
244000 
271000 



104 



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105 
TABLE NO. 48. 



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106 



TABLE NO. 49. 

COST OF KESERVOIES. 

With banks 4, 6 and 8 feet high, and at rates of 6 and 8 cents 
per cubic yard for moving earth. (To cost of embankment 
add cost of outlets, gates, protection for banks, etc.) 





(.'ost, 
at 8 cts 
per yd. 


CC^^lO^OC^OOCJOCSOO 




Cost, 
at 6 cts 
per yd. 


ClCOCCOOKM'-lC-OO 




('u. yds 

in bank 

8 feet 

high 


-^ 00 (M CC CO .->] O t^ lO '— 1 
■'^ -r—l r-i ■—^ i—( \ 




Cost, 
at 8 cts. 
per yd. 


?COO-*QO!:C005:CQOlO 

oooiooioocot-o-# 




Cost, 
at 6 cts 
per yd 






Cu yds 

in bank 

6 feet 

high 






Cost, 
at 8 cts 
per yd . 


lO0i(MO:000(30C-OC0 
O'^OO'— fOlOt-Oli— 'CO 




Cost, 
at 6 cts 
per yd. 


o;G<]i>-aot-ccciC.'5?r-0 
t-i-HCOior— OiOGQCcio 




CuYds 
in bank 

4 feet 
high 


Cg050i'-^'*C00500QOO 

COQ0O]?DO5<M^I>'O5^ 
i-iM(MCClG<i:OCO000O'* 




Area 

in 
Acres 





Note— It is assumed that the price of moving earth will 
be from 6 to 8 cents per yard at which rate (8c) most of the 
sub-contract work on Dakota Ry. grades has been let, the 
lesser rate of 6 cents has, in some cases, been paid. If the 
cost is desired for an embankment of any other size or cross 
section the length may be taken directly from table 45, the 
cross section from table 44 and the cubic yards then quickly 
calculated and multiplied by the price agreed upon, in order 
to get the total cost. This table will answer most purposes 
and will be of value for ready reference. 



107 

Continued from page 100. 

OUTLETS AND GATES. 

OUTLETS. The outlets or culverts through the banks to 
the main ditches should be set before the bank is built and 
with refeference to the location of the ditches. The size of 
the outlet will be governed by the amount of water to be de- 
livered to the ditch. If the ditch is small or short the size 
may be smaller than for a large or long ditch. In the latter 
case make the outlet large enough to deliver the requisite 
amount of water at a velocity not so great as to wash the 
banks of the ditch. The outlets may be made of plank or of 
sewer pipe, the latter being especially good, but, in most 
cases, not so readily obtainable. The earth should be well 
tamped about the box or pipe in order to make a water tight 
joint. 

By reason of the difference in sizes of the outlets, the dif- 
ference in length through banks of different breadths, and 
with the difference in the head due to constant lowering of 
the water in the reservoir, and the different methods of con- 
structing the outlets, no precise data can be given as to the 
relative discharging capacities of different sizes of outlets 
but the following table will give the approximate volumes 
in cubic feet per minute discharged. 

TABLE NO. 50. 



FLOW OF WATER FROM RESERVOIRS. 



Neiv. 



Head of 


Outlet 


Outlet 


Outlet 


Outlet 


Outlet 




water 


12X12 


12X24 


12X36 


24X24 


24X36 




in feet. 


inches 


inches 


inches 


inches 


inches 




2 


400 


800 


1200 


1600 


2400 




3 


500 


1000 


1500 


2000 


3000 




i 


575 


1150 


1725 


2300 


3450 


Cubic ft. 





650 


1300 


1950 


2600 


3900 


per min. 


6 


720 


1440 


2160 


2880 


4320 





GATES. The gates should be set at the the inner end of 
the outlets and a plank walk built from the top of the bank 
leading out over the water to a point over the gate in order 
that the gate may be lifted. In construction the gate is 
most simple; any farmer or carpenter being competent 
to make them. A tightly fitting slide over the end of the 
box or pipe outlet being all that is necessary to shut off the 
water. The gate may be raised or lowered by a stick of 2x4 
bolted to the front of the gate and leading up through slides 
or guide holes in the end of the walk. Simple means too 
may be provided for fastening the gate either up or down. 
The pressure of the water against the gate will keep it in 
position and preserve a tight joint if the sliding surfaces 
have been properly dressed or surfaced. Guides should be 
provided in the sliding supports so as to make sure that the 
gate will return to its seat when it is desired to lower it. 
Modifications of detail are many and will suggest themselves 



108 




to any one as the conditions of the work or the setting may 
require. 

Fig. 16 shows a simple and common form of gate. 



rig. 16. 

Simple form of 
gate. aft=side plank 
of outlet box. 66 
and cc = top and bot- 
tom plank of outlet 
box. e — upright 
plank supporting 
outer end of walk. 
ff — guides for gate. 
s — space in which 
gate slides. ^=gate. 
li = hoisting timber. 



Sub Reservoirs and Storage Ditches. 

As previously stated it may be best to have two or more 
reservoirs on the same farm or under service by the same 
well. These may be on different ridges or knolls and may 
be directly connected with the well or with each other by 
piping, flumes or ditches. A sub reservoir may be provided 
to receive the waters elevated from lower ditches or pools 
by wind mills or water rams. In many cases storage ditches 
will be necessary to give proper service to areas at a consid- 
erable distance from the well or reservoir. A storage ditch 
is merely a big ditch, or one made higher and wider than 
the ordinary main ditch so as to hold in store a large vol- 
ume of water ready for immediate service through lateral 
ditches to the adjacent lands. Such a ditch or canal along 
a quarter line might better serve adjacent farms than a res- 
ervoir of any other form, or if located along the top of a nar- 
row ridge where a large circular reservoir would be imprac- 
ticable or needlessly expensive. 

For the volume of water stored a storage ditch requires a 
greater cubic capacity of embankment and hence a greater 
proportionate cost than a circular reservoir; but the econ- 
omy of space, the lay of the land or the character of the ser- 
vice to be rendered may more than compensate for the in- 
creased proportionate cost. 



109 

DISTRIBUTION OF WATER BY DITCHES, 

FLUMES AND PIPES. 

The water having been obtained and stored the next con- 
sideration is as to its conveyance from the well or reservoir 
to any desired place and then its distribution over the land 
to be irrigated. 

The distinctive feature of the great irrigation systems of 
the west, and of other countries, is the great length, size, 
and expense of the ditches and flumes necessary to convey 
the water from the storage reservoirs or rivers to the low- 
lying irrigated lands. These ditches are often of great size 
and extend for many miles; the cost reaching tens or hun- 
dreds of thousands of dollars. Great viaducts of masonry, 
or trestles of timber or iron, to carry the canal over rivers 
or valleys, deep cuts along the mountain sides, flumes sus- 
pended over or along precipitous canyons, tunnels through 
the rock hills, and enormous dams and head gates are feat- 
ures of great interest, as well as of expense, common to 
the distribution of irrigation waters in regions less favored 
than our own. 

How tame, in comparison, will be the means of distribu- 
tion on the Dakota prairies and under the individual sys- 
tem of irrigation by wells. Our people may well forego the 
glory of being the possessors of world renowned works of 
engineering skill, for the sake of the greater economy and 
the honorable distinction of being the possessors of the 
largest and most fertile valley in America, wherein irriga- 
tion may be more cheaply inaugurated and maintained than 
in any other state- 
All the leading features of other systems, such as dams, 
head-works, main canals, pipe lines, viaducts, &c., will not 
be known here. Probably few ditches will be larger than 10 
feet at the bottom, and but few will be over 5 miles in length. 
Pipe lines will be small, and flumes will be low and short. 
In brief, there will be no heavy or expensive features at- 
tached to the distribution of water in this prairie country, 
and hence the great economy of an irrigation system in 
Dakota. 

The result sought by all systems is the bringing of water 
to the land. 

While it may sound well, or arouse in one the spirit of 
pride, to say that we have the largest dam, the largest or 
the longest ditch, the longest tunnel, or the highest flume 
in the world, it is a distinction the wary capitalist will will- 
ingly forego for the more humble statement that, for a 
given outlay, we have under water a larger number of acres 
than can be shown any where else. This will be the pride 
of the Dakota irrigator. He will point not to his towering 
masonry, not to his navigable canal system, not to his sky- 
scraping trestle-work, nor to the dismal depths of a hole 



no 

through a hilJ, but with pride to his perennial fountain, to 
his simple ditches and to his broad expanse of fertile fields, 
where more that is of profit may be seen, as the result of a 
dollar spent, than can be shown by any of his neighbors in 
other states. 

If this true picture does not soon attract the scrutinizing 
eye of capital, and Dakota ere long become their chosen 
pasture, then, indeed, will all signs fail. 

Water is conveyed from point of supply to place of distri- 
bution in ditches, flumes, or pipes, and is distributed over 
the land through smaller, lateral-ditches or by plow fur- 
rows, by the actual flooding of the surface, or by means of 
sub-irrigation through lines of tile pipes; the latter system 
however, being confined almost exclusively to the irrigation 
of garden and orchard lands. 

Volumes might be written on the subject of water distri- 
bution and allied subjects, but the limit of this little book 
will admit of but brief reference to some of the matters 
most likely to engage the attention of our farmers. 



Form and Size. 

According to a classification adopted by the Census De- 
partment of Agriculture, irrigation ditches are divided into 
three classes. 

First, those under 5 feet in width, 

Second, those from 5 to 10 feet wide, and 

Third, those over 10 feet wide on the bottom, the depth 
in a general way corresponding with these widths being 1 
foot, \% feet, and 2^% feet and over. By reason of the com- 
paratively small volumes of water to be carried, and the re- 
stricted area to be served from any one source, the Dakota 
irrigation ditches will be mostly small; few, it is safe to say, 
need be as large as 10 feet in width. A ditch need be only 
large enough to convey the water to the place whence it is 
to be distributed. By " large enough " is meant, of such a 
size as will deliver the volume of water needed, at a velocity 
not so great as to wash the banks of the ditch, and not so 
large as to present a needless excess of surface of bank, 
which will increase the percentage of seepage, or of surface 
to the air, which will increase the percentage of evaporation. 

In large ditches much depends upon the form or sectional 
outline of the excavation and banks. In smaller ditches 
this is of less importance so long as the fiow is not impeded 
by the roughness of the sides or by the abrupt changes of 
direction. 



Ill 

The same degree of care in the original construction and 
future maintenance of ditches cannot be secured in a sec- 
tion where irrigation is first practiced, and where the new 
Irrigator has yet to learn the importance of close attention 
to details, as in a section where irrigation has long been 
practiced and where each detail of the operation has been 
reduced to a system. 

The sooner attention is given to the careful and workman- 
like construction of ditches, the sooner will the labor devot- 
ed to irrigation return a satisfactory profit. A channel, 
roughly scratched in the ground is not a ditch, and, however 
much the owner may believe in its sufficiency to give proper 
service, the flowing water cannot be deceived and will not 
do its full service until given the opportunity which the 
laws of of hydraulics have decreed. 

The main distributing ditches should be built for perma- 
nent use. The smaller or distributing laterals may, in cer- 
tain cases, be cheaply built to serve the purpose for a season. 
They may be thrown out by a double-mould-board plow or 
as a single plow furrow. The larger sections can be most 
cheaply built with ditching machines. The section of the 
ditch may have the form shown in Fig. 17, where the slope 
of the bank in the cut or excavation is one foot horizontal 
to one foot vertical. The excavated earth may, and usually 
will, be put into the banks as shown at A, ov it may be 
placed as shown at B, where a berm, or ledge, b is left at the 
sides of the ditch. The slope of the banks in the embank- 
ment being 1}4 to 1. 



Fig. 17 

If excess earth is required to build the bank higher or wider 
either theditch may be made wider and deeper or the extra 
earth may be obtained from side ditches or borrow-pits B, 
or by both means. It is the province of the engineer to di- 
rect as to thse details of the work so we will here consider 
only such details as relate to the ordinary work which the 
farmer himself may be required to perform. For all ordi- 
nary purposes of distribution from the reservoirs to the 
more distant laterals, main ditches from 4 to 6 feet wide will 
suffice. (The width of ditch, as stated, is understood to be 
the width at the bottom.) 

The construction should be workmanlike, the bottom even 
and free from sods, stones, lumps, of clay,or weeds; the sides 
smooth, even, and free from like obstructions to the even 
and free flow of the water. 



112 



10' 




B 

average width 
10ft. + 4ft_ 14 



"W c 

raultipiied 



Fig. 18 
by the 



Fig. 18 represents 
the cross section of a 
ditch 4 feet wide and 
having water 3 feet 
deep. The area of 
the wet section of the 
ditch is equal to the 
depth. In this case 



= 7, 7x3=21 sq. ft. 



2 2 ~ *' • /stj— ix 04. it. — area of wet section 

The Wet Perimeter in the length of that portion of the 
surface of the cross-section which is covered by water, AB, 
BC, CD In order to determine this length, the length of 
the slopes A B and C D must be known. These may be 
found, for any depth of water or for any degree of slope — as 
follows: The slope is the hypothenuse of the right-angled 
triangle ABE, and its length is therefore equal to the 
square root of the sum of the squares of the other two sides. 
In this case the sides A E and E B are each equal (the slope 
being 1 to 1) to 8 feet. The sum of the squares of A E & E B 
=9+9=18. The square root of 18 (see table of roots)=4.2, 
which is therefore the length of A B. If the slope had been 
13^ to 1, A E would = 4.5 feet which squared=20.25 which 
+9, the square of E B, = 29.25 the sq. rt. of which=5.4= 
length of A B. So with any other depth or degree of slope. 
In this case the wet perimeter — 4.2+4+4.2=12.4 feet. 

The "mean radius,'' ''hydraulic radius" ""hydraulic mean 
depth" and ''mean depth" are synonymous terms for the 

area of wet cross section area A B C D, ^^ ^^^ 

or ^ i -rt I — -rt,r\ I — 77tv\ ^ ' "'^ ■'^n 



wet perimeter 



(AB^BC-^CD) 



21 so ft 
the above illustration, ^' = 1.69=mean radius. 
' 12.4 

This term, "mean radius," is frequently used in the calcu- 
lation of volumes, grades, and velocities, by Kutter's and 
other formulae and it is is therefore explained, 

Since most slopes will be 1 to 1 or 1% to 1, and most 
depths from 1 to 5 feet, and most widths from 2 to 6 feet, 
the following table has been prepared to show at once the 
lengths of the slopes A B and C D for slopes of 1 to 1, and of 
\}4 to 1, and for depths of 1 to 5 feet; also the wet areas of 
ditches, having bottom widths of 2 to 6 feet, and water from 
2 to 2J^ feet deep; also the lengths of the wet perimeter, and 
the corresponding mean radii. 

Application — The water in a ditch, having side slopes of 1 
to 1, is 3^ feet deep, what is the length of the wetted slope 
A Bf In second column, opposite depth of 33^, is 4.6= 
length in feet required. In third column is 5.8= correspond- 
ing length when slope=13^ to 1. A ditch has 2}4 feet of 
water and a bottom width of 5 feet, what is area of wet sec- 



113 

tion, length of wet perimeter and mean radius? Under 
head of depth of 2^ feet take width of 5 feet; in succeeding 
columns find ^+18.75 sq. ft. , P=12 ft., and R = 1.56. The 
limits of the table will serve for the ordinary range of work 
and will no doubt save some time in making calculations. 

TABLE NO. 51. 

TABLE OF DEPTHS, SLOPES, WET AREAS, WET PERIMETERS AND MEAN 

RADII OF SMALL DITCHES. NeW. 



Slope of bank 
1 hor. to 1 vert. 



I Slope of 
i bk IV2 to 1 



Depth of 

water in 

feet 



Length 
of slope 
(ab) in ft 



1 

1% 

2 

2J4 
2H 
2% 
3 

314 
31/2 
S% 
4 

5 



1.4 

1.8 
2.1 
2.5 

2.8 

3.2 
3.5 
3.9 
4.2 

4.6 
4.9 

0.3 
5.7 
6.0 
6.4 
6.7 
7.1 



Length of 

slope (ab) 

in feet. 



10 ^'-S 



1.8 

2.2 
2.7 
3.2 
3.6 

4.1 

4.5 
4.9 
5.4 

5.8 
6.3 
6.7 
7.2 
7.6 

8.1 
8.5 
9.0 



D. 



w7^ 



IH 

1V2 

J_l_2_ 

2 



2H 
21/0 



Area 


Length 


of wet 


of wet 


section, 


perime- 


sq. feet. 


ter in ft 


A 


P. 


3. 


4.8 


4. 


5.8 


0. 


6.8 


6. 


7.8 


5.25 


6.2 


6.75 


7.2 


S.25 


S.2 


9.75 


9.2 


8. 


7.6 


10. 


8.6 


12. 


9.6 


14. 


10.6 


16. 


11.6 


13.75 


10. 


16.25 


11. 


18.75 


12. 


21.25 


13. 


23.75 


14. : 



Mean 
Ratlins 



.625 
.690 
.735 
■ 76^ 

.847 
.937 
1.01 
1.06 

1.05 
1.16 
1.25 
1.32 
1.38 

1.37 
1.48 
1.56 
1.63 
1.70 



Flow of Water in Ditches. 

This complex branch of dydraulics is treated exhaustively 
in several large works on the subject, it being of prime im- 
portance in countries where water is taken from rivers, or 
from large storage basins, and carried for miles in large 
canals or ditches. Important, because upon its proper treat- 
ment rests the accurate gauging of rivers and canals, or the 
measurement of the volume of water flowing in them. On 
a knowledge of the exact volume of the supply rests the 
matter of the volume of apportionment to different districts 
or ditches. 

Many mechanical divices are used for measuring the vel- 
ocities of running streams, and many formulae and rules 
are given for the calculation of the velocity and volume. 

The Dakota system of irrigation being so entirely different, the necessi- 
ty for the accurate measurement of water in ditches is almost entirely 
done away with ; so but brief mention will be made of a few points in 
this connection. The measurement of most ditches and streams is in the 
unit of the cubic foot per second ; or the number of cubic feet of water 
the stream will discharge in one second. The discharge— for a given depth 
of water in the ditch— will depend upon the slope or grade of the ditch, 
the area of the section, the condition of the bottom and banks, and upon 
the direction and force of the wind, which exerts a considerable effect 
upon the exposed surface of the water. [One-tenth of the width of sur- 
face being allowed for wind resistance.] 



114 

As above explained, the sectional area of any ditch, or of 
the wet section thereof, is equal to the average width x 
by the depth. 

The velocity of a running stream is not the same at all 
points of the cross -section, it being least at the bottom and 
sides, where the friction is greatest, and less at the surface 
than at a point a short distance below it. The point of 
greatest velocity is therefore at the middle of the stream 
and just below the surface. To determine the velocity of 
any stream it becomes necessary, therefore, to determine 
the mean velocity, or such a velocity as would be common 
to all the threads of water of the stream if the discharge re- 
mained the same and all flowed at the same rate. 

Current meters and other mechanical devices are used to 
determine the velocity of the current at several points in 
the cross-section, and from a reduction of these observa- 
tions a mean is obtained for the whole section. 

Intricate formulae are likewise employed to determine 
the velocity and discharge, mathematically; but their ap- 
plication, involving a considerable knowledge of matherjaa- 
tics and hydraulics, they are not popular with the average 
irrigator. The simplest way to determine the approximate 
mean velocity of a stream is to take a certain percentage 
of the ascertained maximun surface velocity. By experi- 
ment the mean velocity has been found to be from 80 to 85 
per cent of the maxinaum >urface velocity. In this country 
80 per cent is usually taken as the standard. To determine 
the maximum surface velocity, select a straight section of 
ditch, in good repair, and stake out a section of 100 feet. 
Place in the current — at a short distauce above the upper 
stake— a small block of wood, so that when it passes the 
upper stake it will have acquired the velocity of the water. 
]^ ote carefully the exact time of its passage of both the up- 
per and the lower stakes, and record the interval. Repeat 
this, say four or five times, and take an average of the in- 
tervals to get the nearest true interval. 

Example, — 1st. interval = 25 seconds. 
2d. " 24 ^' 

3d. " 25 

4th. " 26 " 

100 which H- 4 = 25 sec. = aver- 
age interval. If the current runs 100 feet in 25 seconds it 
runs J^ = 4 feet per second, = maximun surface velocity. 
80 per cent of 4 feet = 3.2 feet per second = the mean 
velocity of the stream. 

The volume m cubic feet discharged will of course equal 
the wet area x by the mean velocity. Assume the ditch to 
be 5 feet wide and the water 2 feet deep. From table No. 51 
we find the wet section to have an area of 14 square feet. 
Then 14 x 3.2 (area X mean vel.) = 44.8 = cubic feet per 
second discharged. Table 36 shows this to be equal to 335 



115 

gallons per second. The section of ditch should be in good 
condition and fairly uniform in section. 

The determination of the velocity and volume, as above 
described, necessitates the measurement of the surface velo- 
city. Where formulae are used this is not necessary. 

As above stated, the use of formulae not being convenient 
to the average irrigator, and the space within the limit of 
this little book being insufficient to properly explain even 
the simpler ones, the subject will not be considered. The 
reader being referred to such standard works as Trautwine's 
Engineer's Pocket Book— where the formula of Kutter is 
fully explained and illustrated by examples and tables of 
coefficients (P. 571 to 2796, in editions of 1888 or 1891); Wies- 
bach's Mechanics, where is found a much simpler formula, 
and one more convenient, with table of coefficients; and to 
the recent exhaustive work of P. J. Flynn on Irrigation, and 
the Flow of Water in Open Canals. (See advertisement of 
Irrigation Age); as well as to any of the many standard 
works on hydraulics. 

Grades. 

A study of the details of the larger canals or ditches of 
the west shows a great variety of sizes and grades, yet more 
uniformity than some would expect. l")itclies running from 
20 to over 100 miles have widths from 20 to 80 feet, some be- 
ing built with, and some without, berms; the grades ranging 
from 1 foot to 7 feet per mile. The steeper grades are not 
common and are for short distances only. The average 
grades for main ditches, carrying from 2 to 6 feet of water, 
are from IJ^ to 2% feet per mile. Such low grades will an- 
swer only for the larger ditches carrying large volumes of 
water and where the ratio of volume to resistance, or friction 
on the sides, is large. 

In smaller distributing ditches, where the volume is small- 
er, and the resistance proportionately much greater, a steep- 
er grade must be allowed. It is frequently said by those who 
are not informed that this country is too level to irrigate to 
advantage. 

Such is far from being the case. The writter has yet to 
find a quarter section of land, in the most level portion of 
the James river valley, that is too level to irrigate. The 
gently rolling lands, or such as have a comparatively uni- 
form slope, are the best located for irrigation. 

The location of the well or reservoir, on or near the high- 
est point, fixes the point of radiation of the ditches, their 
lines being located according to the grades secured and the 
lay of the land to be served. The aim will always be to 
keep the water up as high as possible for it is useless to sac- 
rifice grade or make a ditch run at a greater grade than is 
necessary. It is an easy matter to let the water down but a 
difficult thing to raise it. By keeping the grades up, a broad- 
er area is kept within the range of service. 



116 



Grades ot: from 2 to 5 feet per mile will be ample to secure 
good delivery from the smaller main ditches, while the later- 
als will require steeper grades, which, in many cases, may 
be confined to the approximate level of the field, except on 
hill sides or quite abrupt slopes, in which case the grades 
will be carried around the slope as contours. The following 
table will show the grades per 100 feet corresponding to giv- 
en grades per mile. If the grade per rod is required it may 
be taken approximately from the table by taking ^ of the 
grade for 100 feet. If the grade is required exactly for any 
given distance, and corresponding to any given grade per 
mile, it may be found by simple proportion, thus: 
grade per mile : one mile : : required grade : given distance. 

Example,— What is the grade for 3,500 feet, corresponding 
to a grade of 10 feet per mile? 

10 : 5280 : : ( V) : 3500 = 35000 -^ 5280 = 6.62 = Ans. 
or 10 : 5280 : : 6.62 : 3500. 

That is, the given distance multiplied by the grade per 
mile and the product divided by 5280, the number of feet in 
a mile, equals the required grade. In this way any grades, 
other than those given in the table, may be found. In like 
manner the grade per mile, corresponding to the grade for 
any given distance, would be found, thus: 

grade per mile ( ?) : 5280 : : given grade : given distance. 

TABLE NO. 52. 

Table of Grades per Mile; or per 100 ft. measured horizontally . 

From Traiitwine. 



Grade 
in ft. 
per mi. 

2 

3 

4 

5 

6 

7 

8 

9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 



Grade in feet 
per 100 feet. 



.01894 
.03788 
.05682 
.07576 
.09470 
.11364 
. 13258 
.15152 
. 17045 
.18939 
.20833 
.22727 
.24621 
.26515 
.28409 
.303 3 
.32197 
.34091 
.35985 
.37879 



NOTE. 

If the grade per mile con- 
sists of feet and tenths add 
to the grade per loo ft. as 
given in the first table , 
the grade per loo feet for 
the required tenths, as 
given in the second table. 
Example, Grade per mile 
= 12.85 ft. what IS grade 
per 100 feet and in 725 
ft.? .22727 -|- .01609 — 
.24336 = grade in loo 
ft. .24336 X 7 = 1.70352 
= grade in 700 ft. and 
.24336 -5- 4 = .06084 = 
grade in 25 ft. 1.70352 
-\- .06084 = 1.76436 = 
grade for 725 feet, OR 

•24336 X 7-25 = 1.76436 



Grade 
in ft. 


Grade per 100 
feet. 


per mi. 




.05 


.00094 


.1 


.00189 


.15 


.00283 


.2 


.00379 


.25 


.00473 


.3 


.00568 


.35 


.00662 


.4 


.00758 


.45 


.00852 


.5 


.00947 


.55 


.01041 


.6 


.01136 


.65 


.01230 


.7 


.01326 


.75 


.01420 


.8 


.01515 


.85 


.01609 


.9 


.01705 


.95 


.01799 


1.0 


.01894 



117 
Laying Out. 

The laying out of the ditches is the provience of the en- 
gineer or surveyor, although the more intelligent farmers 
may do much of their own work and thus save considerable 
expense. In the arrangement of fields it may become nec- 
essary to change the location of a ditch or to lay out a new 
one. This work the farmer may do with simple means, al- 
though, in many cases, it will pay an intelligent farmer to 
own a drainage level. Its use on'his own, and on his neigh- 
bors' work, will soon pay for it. Simple devices for small 
jobs will be described later on. 

Something of a knowledge of leveling must be had in order 
to do the work, but sufficient may soon be acquired to per- 
mit of much home-work being done. If any doubt exists as 
to ones ability to lay out a piece of work it will be cheaper 
to hire some one to do it who knows how. 

The running of preliminary lines, making of profiles, cross 
sectioning, calculation of sizes, carrying capacities, and 
grades, and the final location and construction are details 
of the work, each the proper subject of a chapter. The limit 
of this little book will not permit, however, of any special 
consideration of these purely technical details of the work. 
(See remarks on leveling, P. 132 to 134.) 

Excavation and Cost. 

The smaller ditches may be constructed by hand-shovel- 
ing, by plowing and scraping, or by plowing with a large 
double-mould-board plow. The larger ditches by plowing 
and scraping, or by grading or ditching machines. Hand 
work is of course most expensive but it will be necessary in 
some places. Simple plowed ditches are of course the cheap- 
est, as they are also but temporary, and in the end the more 
expensive. Scraper woak will cover the greatest range of 
work and will fairly represent the average cost. Work done 
with a ditching machine is very satisfactory and far cheaper 
than other work. 

The New Era grader and ditcher (see advertisement) is 
the leading machine of its class. It will place in the bank 
from 1000 to 1400 cubic yards of earth per day at a cost of 
about 2 cents per yard; or it will load from 600 to 800 wagons 
per day. It has been used in all states, in all soils, and on 
all classes of work with full satisfaction and great economy. 
Its use on reservoirs is especially recommended. Done with 
a ditcher, the ditches on a section of average land need not 
cost to exceed $200, or f 50 per quarter section. Under fav- 
orable circumstances the work has been done for half this 
sum. (See also page 246.) 

Dakota's soil and topography renders the operation of a 
grader easy, economical and altogether satisfactory. 



118 

No farmer can aiford to buy a machine to do his own work 
alone, but when farmers become associated in the putting 
down of wells and construction of reservoirs and ditches, 
then it will pay to buy machines, for on a large job they will 
soon save their cost. The suggestion is made that town- 
ships or counties purchase not only drilling outfits but also 
ditching outfits. Each farmer could pay for its use on his 
work, at such a rate as would effect a great saviug to him- 
self, and, at the same time, soon return to the township the 
cost of the machine. An additional advantage of such an 
arrangement would be in the use of the grader on the pub- 
lic roads where much cost to the tax-payers could be saved 
thereby. 

In tills, as in all other fields, the machine has come to 
stay as against all other forms of labor. 

The suggestion here made will bear careful consideration 
by associations of farmers or by townships and counties. 

Most of the railway grading in the state has been sub-let 
to farme s and others at from 6 to 8 cents per yard, at which 
rate — and on large contracts, there is only fair wages. 

Table No. 49 shows the cost of grading reservoir embank- 
ments at the rate of 6 and 8 cents per yard. A reservoir of 
5 acres, having an 8 foot bank, would cost $746 at 8 cents 
per yard. Four such reservoirs on adjacent farms would 
cost about $3,000. If done with a grading machine, at a 
cost of even 3 cents per yard, there would, on that small job, 
be a clear saving of $1,500 over other work Such conserva- 
tive illustrations show the value of properly considering the 
means of doing the work. What applies to reservoirs ap- 
plies likewise to ditches. 

Embankments and Footings. 

Under the head "Reservoirs," on page 99, the qualified 
statement is made that the use of drag-scrapers will result 
in a more solid bank than when scrapers or graders are used. 
This is commonly so; bat not necessarily so, for if the grad- 
er-work is properly followed up with a harrow the earth is 
torn, mixed, and more thoroughly compacted than in any 
other way and the resulting embankment is as good as if 
done by any other means. 

The object in any embankment is to have it sufficiently 
solid to hold water. Around gates and outlets the earth 
should be solidly tamped or puddled— wetted down— in 
order to make a tight joint. So, too, with the footings of 
high banks, they require special attention. If the dirt is 
thrown loosely on top ©f the sod the water may percolate 
through the loose, filter-like footing of grass and weeds and 
cause a leak, and possibly a wash-out of the bank. 

To insure against this there should be, along the middle- 
line of every heavy bank, several plow furrows turned and 
the sod cast aside' The fresh earth of the bank settles into 



119 

the trench and soon forms a tight joint with the solid sur- 
face. If the banks are but 6 or 8 ieet high, this will suffice; 
but if they are higher the trench may better be double- 
plowed and a bank of wet earth piled in and over it thus 
insuring a compact core for the bank . 

Reference has been made to the slope of the banks. The 
slope in the excavation need not usually be more that 1 to 1, 
but if the cut is of any considerable depth, and the soil 
sandy or loose, then a slope of m to 1 will be better. 

The slope in the fill or banks may usually be 1^ to 1, but 
if they are high a slope of 2 to 1, on the wet side, will be 
safer. The slopes of the reservoir banks are thus given in 
the diagrams and tables under head of reservoirs. 

Cubic Contents of Excavations. 

Tables giving the cubic contents, per unit of length, for 
ditches of different depths, widths, and slopes, would be con- 
venient for reference, but they would necessarily be long in 
order to cover the whole ground. On this account they will 
be omitted and the simple rule given by which the calcina- 
tions may be made in any given case. 

RULE: Multiply the area of the section of the ditch, in 
square feet, by the length of the ditch, in feet, and divide 
the product by 27 to get the cubic yards of earth in the 
ditch. 

Determine the area of the section as explained in connec- 
tion with table 51. 

Example— How many cubic yards in a ditch 4 feet wide, 
2}4 feet deep, and 1835 feet long ? Bottom width 4 feet+top 
width 83^ feet =121^ which^2=6M=average width. 63^ 
X23=4, the depth, =:14.0625=area, and cubic yards in I ft. of 
ditch. 14.0625X1835, the length,=25,805 cu. ft. which^27= 
956= cubic yards. 

To get the contents of the ditch in gallons, proceed as 
above, using the wet section— and multiply the volume in 
c^^6^c feet by 7.48052 to get volume in gallons. 

Gates. The gates or outlets from the main ditches to 
the laterals are too simple in construction to need illustra- 
tion or special consideration. They may be made with 
more or less complication, but a simple frame of plank with 
a board or plank slide or gate, fitted to slide vertically 
within cleats will answer every purpose. When the gate is 
down— closed — the mud in the ditch may be drawn about the 
base and sides to aid in keeping it water tight. 

In the working laterals, where it is desired either to cut 
oft" any further flow or to dam up the water for the flooding 
of a certain area, a small portable dam or stop of sheet iron 
or wood may be used. In case the water passing from the 
main ditch to the laterals is to be meastired or gauged then 
the common gate will give place to the weir or to the spill- 
box shown in Fig, 6. 



120 

Oae matter will be mentioned as to the location, of ditches 
— the same applymg to both flumes and pipe-lines — which 
is to locate them, as nearly as circumstances of economy, 
grades, &c will permit, on such courses as will permit of the 
proper working of the land. Rectangular areas are the 
most convenient to cultivate, and sharp angular pieces the 
most difficult. 80, in locating water-ways some considera- 
tion should be given to the after convenience of handling 
machinery in the cultivation of the land. A iiiodf-rate in- 
crease of the first cost of the water-way w^ould be justified 
in au effort to secure an area more favorable in form to 
convenient cultivation or access from other parts of the 
land. 

Flumes. 

Flumes are boxes or troughs used to convey water where 
ditches are impracticable or needlessly expensive either to 
construct or to maintain. Where a ravine, valley, or any 
considerable depression crosses the line of a ditch the water 
may be turned into a liume, carried over the depression, and 
then discharged into another ditch on the farther side. It 
may, too, be advisable to carry the water in a fluuie over 
loose, sandy soil, where the loss by percolation would be so 
excessive as to render a sufficient delivery from an open 
ditch either diflicult or impossible. 

Many cases will therefore arise where the use of flumes 
will either save the farmer considerable expense or conserve 
his greater convenience. Special forms of sheet iron, or 
other sheet metal, flumes are much used in mountainous 
sections because of their lightness, tightness, and economy, 
and the facility of erecting them in difficult places. 

As usually constructed flumes are merely wooden boxes, 
open at the top, and of such size and strength as is neces- 
sary to carry and support the water supplied. Many in the 
west are of large size, great strength, and traverse long 
distances and at great height. Such as Dakota farmers will 
use will be small, short and low. The grades may, if neces- 
sary, be somewhat lighter, and the size smaller, than those 
of the ditches supplying them, because of the lesser friction 
and the greater facility of flow. The volume of water to be 
carried will regulate the size the same as in ditches and the 
grade will, in the same way, regulate the carrying capacity 
by increasing or decreasing the velocity of the current. 

The effect of friction of the water upon the sides of the 
flume, and of even a gentle w^nd upon the surface of the 
water, will be quite noticeable— more so than in a ditch. 
An instance is cited. A flume 12 x 18 inches by 800 feet 
long, with a fall of 2 feet, ran to overflowing at the upper 
end while discharging but 3 inches at the lower end. Wind 
and friction prevented the water from running. 



121 

Since the delivery depends upon the vel ocity of flow, and 
since the velocity in an open water-way is due solely to 
gravity, and not to any confined head or pressure, the deliv- 
ering capacity of a flume will be governed by the size and 
grade not by the size of a pipe delivering water to it under 
high pressure. The volume and relative velocities must be 
considered. If the volume to be carried is that of the well 
alone, as where the flume is used to carry the water from 
the Avell to the ditches or the reservoir, the size may be mod- 
erate as compared with that of a flume farther away and 
forming part of the waterway from a reservoir from which a 
much larger volume will flow at one time than would flow 
from the well alone. 

The flume box may be made of 2 inch plank, selected as 
free from loose knots or cracks, closely spiked with 5 or 6 
penny wire spikes (wire spikes will hold better than others 
and are less apt to split the wood in driving.) 

If a small box is needed a single plank of 14 to 18 in. will do 
for the bottom, and similar ones for the sides. The addition 
of a second plank to the bottom, the sides remaining the 
same, will double the volume and a little more than double 
the carrying capacity of the flume,and at but slight increase 
of expense for the supports, braces, etc., may remain sub- 
stantially the same. The construction of a flume is but a 
simple matter. Any carpenter or intelligent farmer can 
build one. 

The supports may in many cases be a single line of heavy 
fence posts, which may be had in lengths as great as 12 or 
14 feet. The buts set 2 or 3 feet in the ground, and well 
tamped, give a good foundation. The grade line for the 
tops is marked by leveling, and the tops then sawed to 
grade, the caps or cross bars spiked to the posts, and the 
flume then constructed on these. If of 6 feet or more in 
height the posts and cross bars had better be braced to pre- 
vent the rocking of the flume by heavy winds. 

Where greater heights than 10 or 12 feet are met a trestle 
of timber posts, properly footed, braced, and anchored, will 
be used. The rigidity of the supporting posts should be 
carefully looked to in tjiis country of almost constant and 
heavy winds, for upon this will depend very largely the 
tightness of the flume and its freedom from leakage. 

The planks, before being spiked together, should be paint- 
ed along the edges in contact, with a coat of very thick 
paint. This will not only aid in making a water tight joint 
but will preserve the wood at the joint. The edges of the 
planks should be dressed true so as to fit properly. As 
rough sawed by the mill they are often wavy or uneven. 
Cut out all warped or crooked pieces for they cannot be 
worked in to advantage. 

If double widths of plank are used on the bottom or sides 
they should be tongued and grooved if possible, or at least 



133 

carefully matched and secured in close contact by cross 
pieces. The joints of the plank at the "bents" or supports, 
will be protected by side strips or braces and the box, at in- 
tervals between the bents, will be surrounded by strips or 
wooden braces to give rigidity to the flume and prevent 
loosening of the joints. 

The length of the space between the bents will depend 
somewhat on the style of the flume or upon the length of 
the lumber used. Where a single line of posts is used have 
the bents at the ends and middle of each length of 16 or 18 ft. 
plank (8 or 9 foot spaces.) If the flume is more solidly built 
20 foot lumber may as well be used, leaving 10 foot spaces. 
If the ditch is large, and the flume correspondingly large, 
the trestles must be heavier and a line of stringers will sup- 
port the flume between the bents. 

The dressed surface of the lumber will be on the inside of 
the box to present as smooth a surface as possible to the 
running water. After the completion of the flume go over 
all the joints with a coat of thick paint applied with an old 
stiif brush. By so doing, and using care and plenty of nails, 
a box may be made that is perfectly v\'atei tight. A small 
leak may often be stopped by filling the crack with stiff clay 
or mud. The details of construction will depend somewhat 
upon the builder and his means, but they are so simple as to 
render further suggestion unnecessary. 

PIPES. The use of pipe-lines for conveying water, in the 
place of ditches or flumes, has increased much since the in- 
troduction of certain cheaper forms of pipe. In the west, 
pipes of wood, banded with iron, are extensively used as are 
pipes of spiral-riveted or welded iron or steel. These latter 
combining great strength with lightness and economy. 

Where waters can be forced under heavy pressure, as from 
our wells, the use of surface pipe-lines of light pipe will find 
a broad field of usefulness and should receive such consider- 
tion as its merits deserve; especially where the work of con- 
structing ditches or flumes is of any special magnitude. 
The pipe-line is intended to take the place of the main ditch 
or flume and not of the distributing laterals. The advant- 
age of a pipe-line over a ditch lies in this — that the water 
supply is not reduced by seepage or evaporation and the 
duty of the well is thereby increased. The area of surface 
occupied by the pipe line is not nearly so great as the area 
occupied by the ditch and embankments and thus the area 
subject to cultivation in increased. The cost of mainte- 
nance is less, for a pipe-line will need but little attention, 
whereas, ditches, however well they may be made, 
will require an annual overhauling; especially if made of 
loose or sandy soil which in a windy country soon blows 



123 

down. The matter of grade is of no importance for the wa- 
ter, being forced, will run up hill as well as down and the 
pipe may be laid to the grade of the surface and deliver 
water at a level higher than the well. The area under ser- 
vice from the well may thereby be increased by rendering it 
possible to reach areas to which gravity alone would not 
carry the water. In this way a well owner may be enabled 
to sell and deliver water to a neighbor whose land lies, or 
is controlled from a higher level. The advantage over a 
flume lies in the fact that evaporation and leakage are done 
away with. The delivering capacity is greater because un- 
der pressure. The first cost may be less even than that of 
the flumes, and the cost of maintenance less. The matter 
of grade is eliminated and the line is on or near the surface 
where it may be more easily constructed or repaired and 
where less liable to damage from winds. The alignment, or 
location, too, may be accommodated to the circumstances of 
the surroundings more readily than that of either ditches or 
flumes. 



It is here assumed that the pipe line connects with the 
well; otherwise there could be no pressure upon the pipe 
and it would stand, in relation to delivery, on a plane with 
the ditch or flume. 

If the line is accommodated to the surface and there is any 
inverted or downward bend in the pipe there should be a 
valve set at the lowest point to permit of emptying or drain- 
ing the pipe during the cold weather or for repairs. The 
pipe may be laid on or near the surface on low supports of 
such form and material as circumstances may suggest. It 
should, at suitable intervals, be fastened or anchored down 
in some suitable way to prevent displacement by the wind 
or by other means, and it should be painted to preserve it 
from rust. 

The concluding remark as to location of ditches may be 
again referred to in this connection, and the suggestion 
made that the location of the lines of the water-ways be 
made as far as possible along the lines of the fields or along 
fences or roads. In the case of the smaller pipe-lines the 
fences themselves will often serve as sufticient and conven- 
ient supports for the pipe, intermediate supports being set 
if necessary. In view of the advantages possessed, under 
certain conditions, by pipe-lines over other forms of water- 
ways one should fully consider the advantages of each as 
well as the cost and maintenance before deciding which to 
adopt. On most lands there will be no use for either pipe- 
lines or flumes. Their service is justified only by the circum- 
stances of the topography and service. 



124 

HYDRAULIC RAM. 

The occasion will frequently arise where the area to be 
irrigated is divided by a water course, gully, or other depres- 
sion, the land on the side of the well and reservoii sloping 
gently toward the " draw, " the opposite side of which is high 
and comparatively level. The well and reservoir being at a 
distance from the draw it will hardly pay to lay a pipe line 
to serve the other side and the water cannot be carried 
across by ditch or flume. How then can it be delivered into 
a ditch on the opposite and higher ground? By elevating it 
only. This could be done from the end of an open ditch on 
the low side by means of a steam or wind pump. The for- 
mer way, by reason of fuel and attendance, would not prove 
profitable, and the latter way possibly ineffectual in spite of 
an abundant supply. A simple and inexpensive water 
elevator may be had in the hydraulic engine or ram which 
may be so set as to take the supply from the open ditch, 
with a fall of such an amount as the slope will permit, leav- 
ing drainage away from the ram. 

By this means the water may be forced across the draw in 
a constant stream, working night and day, rain or shine, and 
without fuel, attention, cost, or care. 

The Rife's Hydraulic Engine (See advertisement, P. 214) is 
such a machine and one of high efficiency. The Xo. 40 ma- 
chine is fitted with a 4-inch supply pipe and a 2-inch dis- 
charge pipe, and, with a fall of from 4 to 6 feet, it will raise 
from 60 to 70 gallons per minute to a height of 20 feet or 
more, and lesser volumes to much greater heights. The 
machine will work under heads of but one or two feet and 
in such cases it could often be used to advantage along side 
slopes to raise a supply of water to a ditch at a higher level. 

Such appliances, together with wind mills and steam 
pumps, will, in the near future, find a welcome place among 
Dakota irrigators, for, although a well will do almost any- 
thing within its immediate reach, there will be duties to 
perform in connection with a properly managed irrigation 
system which are outside of the sphere of the well itself, yet 
properly within the sphere of other appliances, all of which 
must be considered if the greatest good is desired and 
secured. 

PUMPS. 

While this little book is devoted most especially to a con- 
sideration of artesian wells as a source of water supply for 
irrigation, it must not be forgotten that there are other 
sources of supply. Dakota has few lakes or rivers from 
which any supply could be drawn, except of course the 
Missouri, the supply from which is practically inexhaust ible. 

There are many sections all over the states where large, 
shallow wells may be sunk into the sand and gravel beds 



125 

from which an almost inexhaustible water supply may be 
obtained. It must of course be elevated by artificial means 
and the question will at once suggest itself as to whether it 
will pay to do this. 

Yes, It Will Pay! 

As to this there can be no question, and ere long this 
source of water supply will cut a very large figure in the ir- 
rigation of lands in Dakota. 

Certain very erroneous and misleading statements have 
been made by government specialists and agents as to the 
relative value of these phreatic or sub-surface waters, and 
the true artesian waters; they claiming that by far the larger 
supply was the sub-surface supply. These statements and 
reports were founded upon observations elsewhere than in 
Dakota, and upon a woeful lack of personal knowledge as 
to our true artesian supply. The sub-surface supply, while 
no doubt of vast extent and importance, cannot be compared 
with the artesian supply in its extent, universality, volume, 
or the ultimate economy of obtaining it. In other words — a 
given volume, in a given time, may be obtained more cheap- 
ly from an artesian well than from any sub-surface source 
by whatever means it may be secured. 

Notwithstanding this great percentage in favor of the 
artesian supply the other sources should by no means be 
neglected or overlooked. The value to the state of the phre- 
atic supply will be beyond calculation if the people will but 
seek its development. 

As before stated it must be secured by mechanical means; 
either by wind or by steam power. Many farmers— most of 
them — cannot raise the means necessary to put down an 
artesian well, but there are few who cannot raise enough to 
put in a pumping plant at an expense of but a few hundred 
dollars. 

Reference must again be made to the west where the 
manufacture and use of water-elevating machinery is a very 
large and rapidly growing industry. Many sections of coun- 
try cannot be supplied by water taken from streams by 
ditches, so the water must be elevated. Thousands of wells 
have been put down in the several >vestern states and terri- 
tories from which the water will not fiow so it must be 
pumped. This industry is most fully developed in Califor- 
nia and in Colorado. The following illustration will show 
the comparative economy and great value of such means. 

A pumping plant, with a 50 horse-power engine, will raise 
7,500,000 gallons of water to a height of 10 feet in 10 hours. 
This amount of water will cover 28 acres to a depth of one 
foot. The cost of the plant would be about $3000. One 
man can operate it with about one ton of coal per day. 
While so large a plant would not be in order except where 
the supply was very large, a plant of proportionately less 



126 

capacity and cost would accomplish proportioD ate results. 
Many places may be found from which enough water may 
be pumped to irrigate a quarter section of land. 

The question would follow as to the means to be used in 
raising the water to the surface in the greatest volume and 
at the least expense. The author knows of no better means 
than the use of the PULSOMETER or the NYE VACUUM 
steam pumps which possess features especiallj- adapting 
them to such uses. They are both vacuum pumps, having no 
pistons or machinery to wear out or become deranged, are 
exceedingly simple, strong, and eflicient, and, above all, are 
standard the world over; being used for irrigation purposes 
in many countries. All that is needed is the pump, a steam 
boiler, and a little pipe. There are hundreds of thresher 
engines in the state that could be used to supply steam, and 
straw being used as fuel the expense of running would be 
but nominal. 

A No. 6 Pulsometer pump throwing 300 gallons per min- 
ute (18,000 gallons per hour) would cost about $225; an en- 
gine to supply steam could be rented during its period of 
idleness and could be run at an expense of but $2 or $8 per 
day for fuel and attendance. Surely, then, here is a most 
valuable auxiliary supply in the irrigation field of Dakota, 
and a means of utilizing it not heretofore presented to our 
people. 

The cost of starting the plant— buying the pump, pipe and 
fittings, digging and connecting 2 or 3 large wells and get- 
ting the boiler need not cost over $1000, yet on such an out- 
lay of capital enough may be easily made in any one year 
to pay the cost of installation and enough surplus very soon 
accumulated to warrant the sinking of an artesian well. 

The increased service rendered by a well, as the result of 
a given outlay or cost, renders that means, or source of sup- 
ply, cheaper in the long run, as it is otherwise the basis of 
more extensive operations; but if the greater source is be- 
yond one's financial reach then by all means grasp at the 
lesser and use a pump. 

WIND MILLS. 

In the utilization of this sub-surface supply the agency of 
wind mills may be made to play an important part and this 
is especially true in this country of almost constant winds. 
A wind mill may supply water for a very considerable area 
of garden and orchard, and, if reinforced by a proper water- 
elevating device, as to which there are several good ones in 
the market, and also a storage reservoir, the area of service 
could be very greatly extended and the profit of the farm 
greatly increased. This means, too, deserves the careful 
consideration of our farmers. 

Get the water from the most available source and by the 
most efficient means. Only get it! for to get it is to 
acquire a competency. 



127 

Wherever a deposit of sand or gravel is found, or where 
wells wherein there is a flow or current — in and out— are 
found, there is to be found, beyond much doubt, a supply 
which would abundantly serve the land upon which the 
supply is found. Every farmer should take some pains to 
investigate the extent and character of his sub -surface sup- 
ply with a view to its future utilization. 




Fig. 19. 

Showing the Pulsometer Pump as set for taking water from a 
stream for the use of irrigation. The view shows the extreme simplicity 
of the plant which renders it especially applicable to use where skilled 
labor or attendance is lacking. Any man can run it or set it up. 
[See next page and page 244.] 



138 




Fig. 20. 

Fig. 20. Shows a No. 6 Pulsometer [capacity 18,000 gallons per hour] 
throwing a stream 46 feet high through 160 feet of 3^2 inch pipe, into a 
flume on top of the bluff. The pump irrigates 1400 fruit trees, uses about 
Vs cord of soft wood per day and is operated by an Indain boy. The plant 
is in Idaho. 

A No. 9 pump, on a lift of 102 feet, used M cord of wood in 10 hours and 
delivered 60,000 gallons per hour. [See page 244.] 



129 

LEVELING. 

It would require more space, diagrams, and illustrations 
than can be here given to fully treat of the different kinds 
of levels, their adjustment, use, and care; and to describe 
and illustrate the many nice points in the art of leveling. 
Much of this techincal information may be had from the 
pamphlets issued by level manufacturers and supplied with 
the instruments. 

Enough will be given to convey to any person of average 
intelligence so much of a knowledge of the art as is neces- 
sary to aid in doing such work as may arise about the farm, 
and yet such as it would not pay to hire an engineer to do, 
even if one were to be had ai call. The principle of level- 
ing is to reduce the inequalities of the surface to a uniform 
plane, or to determine the position of a succession of points 
with reference to a uniform plane. 

Datum Plane. 

It is apparent from this that some plane of reference 
must be chosen which shall be that to which all other points 
are referred iSuch an arbitrarily selected plane is called the 
Datum Plane, or plane of reference, and it is assumed to lie 
at a considerable distance below the surface in order that 
all points referred to it may have plus (+) elevations, instead 
of some plus (+) and some minus ( — ) as would be the case 
if some portion of the line to be run sank below the level of 
the datum plane. 

In a rough or mountainous country 500 or 1000 feet is 
taken as the depth of the plane of reference. In this level 
country 100 feet will be sufficient. That is, in starting any 
piece of level work assume that the starting point is 100 feet 
above this plane, or at an elevation of 100; then proceed to 
get the elevations of all other points, whether higher or 
lower than the starting point. Before describing the opera- 
tion of leveling let us very briefly consider the level or level- 
ing instrument. 

THE LEVEL. 

The engineer's level is a telescopic tube carried in Ys or 
collars, and having a long level-bubble tube attached, 
mounted on a horizontally revolving cross-head which is ad- 
justed and maintained in a level or horizontal position by 
four leveling-screws attached to the head of the tripod on 
which the instrument rests. Cross hairs in the tube give the 
exact center and the horizontal line of sight. Such are the 
main features of a level, and all are constructed on the same 
general plan. 

Some instruments are made with a less powerful and 
shorter telescope, with fewer parts, lighter weight, and 
cheaper in price. Levels of this class known as contractors, 
builders or architects levels are far cheaper than larg- 



130 



er engineer's levels but they are finely constructed and good 
for all classes of work. 

A still cheaper grade of level is the so called *' drainage 
level " which is made for the express purpose of farm use 
inlaying out drains and ditches. In' this special class of 
instruments there is a wide range of design and price, the 
latter ranging from $10 to $30. (The manufacturers, Buff 
and Berger, W. and L. E. Gurley, and Young and Sons, 
whose advertisements appear herein, are leading makers 
of the finest instruments and will supply anything in the 
level line.) 




A $35 or $50 instrument will do good work and last a life- 
time, if properly cared for. One who can use a level will 
soon pay the cost of a good one by home-work. If no good 
level is at hand a simple one, for rough work, may be made 
out of three pieces of board as shown in Fig. 21. 

Take two pieces of nar- 
row board, AB and AC, of 
exactly equal length and 
form as shown, and hav- 
ing a span from B to C of 
10 feet [one of I6I/2 foot 
span— 1 rod — may be more 
convenient.] At exactly 
equal distances from A, 
measured along the 
sides, attach the cross 
stick D. Fasten on the 
plumb line and bob P and 
then adjust the zero point 
O as follows: Drive two 
stakes in the ground, as 
supports for the level, 
having one of them 2 or 3 
ins. higher than the other. 

Set the foot C on the higher stake and mark upon D the ex. 
act point where the line cuts the edge — as at x. Then re- 
verse the level, end for end, so foot B is on the higher stake, 
and again mark the point where the line cuts D— as at y . 
Draw o just midway between these lines. Then whenever 
the plumb line cuts this o mark the feet.B and C are on a 
level. In one foot a large screw may be set, as shown in the 
enlarged view at S. When screwed in flush the level is set 
for level work but when screwed out the level is set for run- 
ning grades. Thus— if a ditch has a fall of 1 foot in 500 
feet the screw would be turned out slightly over ^ inch . 
The level would be set 50 times in the 500 feet (it having 10 
foot span.) so ^ of 1 foot would be the grade for each setting. 

Such a tool is of course crude but, if well made. and skill- 
fully handled, it will yield quite good results. Other simple, 
home-made levels are frequently described but this is as 
g|)od as any. Get a good level if possible and learn to do 
good work with it. It will pay you if you do much irrigat- 
ing. 



Fig. 21. A simple form of level. 



THE ROD. 



131 



The level rod is a rod of dry wood from 8 to 12 feet long, 
marked into feet, and tenths and hundredths of feet, meas- 
uring upward from the bottom of the rod. The rod may 
have a target or be what is called a "self-reading" rod. The 
target rod has the graduations cut into the wood and the 
distances indicated by figures as at A, Fig. 22, the feet in 
large red figures and the tenths by 
smaller black figures. The leveler 
views the cross lines on the target and 
the rod-man takes the reading as indi- 
cated by the target. (In the Fig. the 
target reads 4 feet) 

The self-reading rod needs no target, 
for the leveler takes the reading from 
sight at the instrument, the gradua- 
tions being made visible by painting as 
shown at B, Fig. 22. Here only the 
feet are numbered, the smaller gradu- 
ations not requiring it. 

Thus, if the horizontal hair of the 
level cuts at the following points on the 
rod the reading would be as follows. 
Refer to B in the Fig. 

1=1.0 feet. 4=1.5 feet. 
3=1.05 " 5=1.75 " 

3=1.3 " 6=1.85 " 

The reading to .05 feet being easily 
made, and, on short sights, a finer read- 
ing may be approximated although a 
reading of less than .05 is not necessary 
except in very fine work. 

Such rods can be easily and accurate- 
ly made by any intelligent person, and 
at a cost of not over one dollar. The 
target may be made of sheet brass or 
of galvanized iron. 

LEVELING. 

Leveling is verj' simple work, and the keeping and reduction of level 
notes equally so. The first thing to do is ro set up and level the instru- 
ment and to select the HUB or starting point. The form of note-keeping 
and the order of procedure is shown on the next page. In this sample 
page from a note-book the following is the significance of the letters head- 
ing the several columns. Stn. = Station Number ; B. S. = Back Sight 
fsometimes called + Sight] ; H. I. = Height of Instrument ; F. S. = Fore 
Sight [sometimes called — Sight] ; Elev. or Ht. = Elevation or height of 
Station ; Rem. = Remarks. 

The hub, or starting point, which may be any permanent object, or a 
stake driven for the purpose, is assumed to have an elevation of 100 feet 
which fact is entered in the note-book as shown. The rod now being held 
on this hub the line of sight of the instrument, or the plane passing 
through its center, strikes the rod 4 feet from the bottom. Enter this un- 
der B. S. as shown. Now if the hub is 100 feet and the instrument reads 4 
feet above it. the center of the instrument is evidently on a plane or level 
of 104 feet [so that Elev. added to B. S. = H. I. or 104 ft.] The H. I. being 
known the height of any other point is found thus — . The rodman goes 
to station 1 and the leveler reads a F. S. of 5.20, which he enters as shown 
under F. S. 




Fig. 22. 
Leveling Rods. 



132 
SAMPLE PAGE FROM LEVELER'S NOTE BOOK. 



Stn. 


B. S. 


H.I. 


F. S. 


Elev. 


Rem. 


Hub 


4.00 


104.00 




100.00 


Hub near well. 


1 






5.20 


98.80 




3 






6.00 


98. 




3 






7.55 


96.45 


T. P. [turning point.] 




7.35 


103.80 


8.80 


95. 


Hub, at barn. 


4 






2.60 


101.20 




5 






1.50 


102.30 


T. P. 


6 


1.20 


103.50 


8.60 


94.90 




7 






2.10 


101.40 










1.70 


101.80 





If the instrument is on a level of 104 ft., and the reading 
on the rod at Stn. 1 is 5.20, it is evident that Stn. 1 is 5.20 ft. 
lower than the instrument. The level of Stn. 1 is therefore 
found by merely subtracting the F. S. reading on that Stn. 
(5.20) from the H. I. (104) = 98.80— which enter as shown. 
In like manner readings are taken at Stns. 2 and 3 which re- 
sult as shown in the notes. From where the instrument 
now stands stn. 4 cannot be seen so the level is moved to a 
new position from which stns. 4 and 5 may be seen. Set up 
and adjust as before. 

The rodman having staid at Stn. 3 the level er now takes a 
B. S. reading on that point. The reading of 7.35 is entered 
as a B. S. Stn. 3 (T. P., or turning point) having an Elev. of 
96.45 and the B. S. equaling 7.35 their sum, or 103.80, will 
give a new H. I. or plane of reference. 

Before proceeding to take the level of Stn. 4 the leveler 
deems it best to take level on some new hub so that in case 
the original hub is moved or destroyed he can relocate his 
work from the new hub. The rodman sets up on the barn 
floor and the leveler reads 8.80 which substracted from 103.80 
=95 as the Elev. of the barn floor. 

He then proceeds as before to take the elevations of other 
stations and to set such other hubs as he may desire. From 
this explanation may be drawn the whole secret of leveling 
and note keeping. 

The Elev. of any starting point added to the B. S. reading 
on that point give the H. I. and any F. S. x^?L^mg subtracted 
from the H . I. gives the Elev. of the point on which the 
reading is taken. Any number of F. S. readings may be 
taken from one setting of the instrument so long as the 
range of sight is clear. Thus, the instrument may be set at 
or near the center of a reservoir and the levels taken at all 
points about the bank without moving. 

Aim, however, to have the lengths of B S and F S courses 
as nearly equal as possible in order not to magnify any 
slight error in the adjustment of the instrument. 

Note especially one fact— as the grade or level runs dozen 
the target or reading runs up on the rod; that is, it takes a 
greatar length of rod to reach from the plane of the instru- 



183 



ment clown to the surface. The reverse is also true 
surface rises the reading on the rod loicers. 



-as the 



To SET A LINE OF STAKES ON A LEVEL. 

Set one stake at the level desired, set the rod on this stake 
and clamp the target on the reading. Proceed then to set 
other stakes, tapping each one down until the target— set on 
the stake — comes into the plane of the instrument. 

To SET A LINE OF STAKES ON ANY GRADE- 

Set and get level on first stake. Suppose now that the 
grade runs cloion at the rate of .1 ft. in 50 feet and that the 
stakes are 25 feet apart. Move the target up on the rod .05 
ft., clamp it, and set the second stake by it. Move it up 05. 
again and set the third stake; and soon to the end. Had 
the grade ran up then the target would have been set down 
at each setting. 

If, instead of setting long stakes to the line of the grade, 
short ones are set, the level of each short stake may be taken 
and then from the notes the height of the grade-line above 
or heloiD each stake may be estimated and indicated. 

Many complications will arise in any extended practice 
but the principle is the same and the specimen notes given 
embrace the secret of the whole operation. If care and 
judgment are exercised fairly good work may he done by 
one not skilled in the work. 

For still further illustration the notes are here given of 
the level- work in the laying out of a reservoir. A reservoir 
of but 13^ acres will be taken for illustration. Stake out 
the circumference, on the center line of the top of the bank, 
into sections of 50 feet each (except where otherwise stated 
in the notes) — circumference being 905 ft. 

Level Notes —Laying out a Reservoir- 



Stn. 

Hub 

1 
2 
3 
3+30 

+60 
+90 
4 



Stn = 105 ft 

1 



B. S. 


H.I. 


5.2 


105.2 



















































F. S. 



5.0 
5.5 
6.2 
7.6 
10.2 
7.5 
6.6 
4.2 
3.2 
4.4 
4.8 
4.8 

5.0 



Elev. 

100.0 

100.2 

99.7 

99.0 

97.6 

95.0 

97.7 

98.6 

101.0 

102.0 

100.8 

100.4 

100.4 

100.2 



Height to Grade. 



106.0 
5.8 
6.3 
7.0 
8.4 
11.0 
8.3 
7.4 
5.0 
4.0 
5.2 



5.6 
5.6 

5.8 



Set up near the center and proceed to take the level of 
e ach stake; first having set a reference hub at some conven- 



134 

lent place outside of the reservoir, the height of which call 
100 ft., which, added to the B S of 5.2=105.2=the H I. The 
notes show a gradual descent from station 1 to a point 30 ft. 
beyond stn. 3 at which point there is a sudden descent into a 
shallow "draw", the bottom of which is at 3-f-60. Thence 
there is a sudden rise to 30+90 and then a gradual rise to 
stn. 6, where the highest point is reached, and thence a grad- 
ual fall to stn. 1 where, on a reading of 5.0, the level is 
found to check with the beginning of the work. 

In looking over either the F. S. readings or the Elev. re- 
sults one may readily see, in the imagination, a profile of the 
work without platting it on paper. 

Assume, now, that the top of the bank will be 4 feet above 
the highest point, at stn. 6— the elev. of which is 102 ft , 
then the grade-line will be on a level of 106. Enter this in 
the last column as shown. It is apparent that the height of 
the bank at each stn. will be the difference between the level 
of that stn. and the level of the grade-line; therefore, sub- 
tract the height or elev. of each stn. from the grade-height 
(106) and the remainder will be the height of the bank at 
that stn., which enter as shown in the last column. 

The staking out of the toe or base of the bank on the in- 
side and outside may now be done since the height and 
slopes are known. The inner slope being 2 to 1 and the 
outer slope 13^ to 1 measure off from each stake, toward and 
from the center of the reservoir the bottom widths occord- 
ing to the height of the bank at that point plus % the width 
of the top of the hank. Thus — at stn. 4. the height being 

7.4 ft., the distance to the inner toe would be 7.4x2=14.8+ 

2.5 (% top)=17.3 ft. The distance to the outer toe would be 
7.4X1.5>=11.1+2.5=13.6 ft., a total width of 30.9 feet. 

The estimate of the number of cubic yds. of earth in the 
bank may be done with suflficient accuracy by assuming the 
cross-section to be level and the height of the bank in each 
section as a mean or average of the end heights. Thus, the 
height at stn. 6 is 4 feet; and at stn. 7 it is 5.2 ft. The aver- 
age height may be taken, therefore, as the height of the 
full stn., 4.0+5.2=9.2-^2=4.6=average for 100 ft. 

Get area of section of this height, and compute cu. yds. 
for 100 feet as explained under head of " Eeservoirs. " Do 
the same for each stn., add the sums to get the total cubic 
contents. 

This, it is believed, will make clear what is really a very 
simple operation and will enable any farmer to do, or to aid 
in doing, part or all of his own work. 

With three sticks, a ball of binding twine, a few stakes, 
and a hatchet, with a little good judgment and eare thrown 
in, any farmer may do in two hours what it would cost him 
$5 to $10 to have done-— and still not be overcharged. Do 
some level practice, if only for exercise. 





— 


1 : 


~ 7 


"~ o 




>« 


O 

A 


= — 5 


4 


1 — 


4 


jt 


_ 4 


O 


/? 


— >5 


o 


*J 


j«r 


~ /9 




1/ 


O 


~ 'y 


_ 1 


T/l 


~ A 


<j 


11 


~ Q 


- lO 


JLL 

72 ~ 


INCHES 


TENTHS 



135 
Fig.23. 

DECIMAL AN D DUODECIMAL SCALES. 

True and Apparent Level. 

Brief mention only need be made of 
the difference between true and appar- 
ent level. In ordinary leveling opera- 
tions no account is taken of the curva- 
ture of the earth. 

True level is a water-level which is the 
true curvature of the earth. 

Apparent level is a horizontal plane 
tangent to the plane of true level at any 
point and extending indefinitely into 
space. 

In leveling the sights are short and 
constitute, therefore, a succession of tan- 
gent planes which closely approximate a 
curve of true level. The difference be- 
tween a curve of true level and a plane 
of apparent level is about 8 inches per 
mile [7.98 ins. or .667 ft] and increases as 
the square of the distance; being 4 times 
8 inches in 2 miles, 9 times 8 inches in 3 
miles, etc. 
Measurements. 

;N early all measurements in engineer- 
ing work are made in feet and decimals 
—tenths and hundredths— instead of in 
feet and inches. This is especially nec- 
essary in leveling. Table No. 67, show- 
ing the decimals of a foot corresponding 
to each g^ of an inch will be of conven- 
ience in the conversion of measurements 
from one unit to the other . For ordin- 
ary work the decimal corresponding to 
the nearest half or quarter inch will be 
close enough. To aid in getting this at 
a glance Fig. 23 has been prepared show- 
ing (in % size) a foot measure divided 
into inches and eighths; and, on the op- 
posite side the divisions to tenths and 
hundredths. This will be of much use 
to the leveler in certain work . 

Examples. — 6 inches = 5 tenths. 

9 " =75 hundredths. 
10 " =83 " 

and 7 tenths = 8% inches. 

25 hundredths = 3 inches, &c. 
The scale may be more readily used than a table. 
The unit of measurement used by the govern- 
ment in surveys of the public lands is the chain 
of 66 feet,— 4 rods— this being divided into 100 
links of 7.92 inches each. For rules as to the 
conversion of chains and links to feet, yards, &c., 
see'" Mensuration" and table of multipliers. 



136 



VALUE OF WATER, VALUE OF LAND 

AND SIZE OF FARMS UNDER A SYSTEM 
OF IRRIGATION. 



VALUE OF WATEE. 

Water for irrigation has a double value. 
First. The first cost of getting it upon the land, or the 

value of the Water rigid. 
Seco7id. The annual rental value. 

Table No. 53, on the opposite page, shows statistics as to 
values, etc., which are official and as accurate as only the 
Government could secure. The table contains much of value 
and deserves careful study. 

The first cost of securing a water supply or right will de- 
pend upon the supply, the distance it must be brought, the 
manner of bringing, etc. All the expense of dams, head- 
gates, ditches, flumes, pipe-lines, or tunnels must be born by 
the area served, so all these expenses enter into, and form 
a part o f, the first cost per acre of a water right. The value 
of the right being such an amount as will pay all the ex- 
penses and leave a proper margin of profit. This value 
ranges from a mere nominal price to $30 or more per acre, 
but averages as shown in the table. The right attaches to 
the land and passes with the title thereto. Once paid for it 
is perpetual as a right, but the continued enjoyment of that 
right is contingent upon the performance of other conditions 
— as the payment of an annual tax for the use of the water, 
or the performance of certain labors in maintaining the 
ditches. 

The amount of the value of the water right may usually 
be considered as the value of the laud, for, as a rule, the 
land has little or no value without the right. 

As touching most directly upon the value of well-waters 
reference may be made to the Gage group of 29 wells near 
San Bernardino, California. They are within a radius of 1 
mile, are from 4 to 10 inches in diameter and have an aver- 
age daily flow of about 33 miner's inches, (about 300 gallons 
per minute) or a total of 954 inches, (about 8600 gallons per 
minute.) One inch is apportioned to 5 acres and is sold as 
high as $250 an acre, or $1250 an inch. The average price 
thereabouts being $1000 per inch. At this rate the total flow 
is worth $954,000 and it will water nearly 5000 acres. 

Four good Dakota wells will throw more water and will 
serve more land. Such being the case one Dakota well of 
2200 gallons per minute would, according to this accepted 
California estimate, be worth S238,500. (Continued on P. 138.) 



137 
TABLE NO. 53. 



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138 

It is not the intention to place such values on wells that 
can be sunk for 83000 or $4000 yet such is their legitimate 
value as compared with values elsewhere. 

Our wells possess values far in excess of their cost, and 
far greater than even their owners now dream of. A good 
well is really a fortune to its owner. 

In Oregon, on one large tract, the annual charge is $3.00 
per acre for 1 foot depth of water (1 acre foot) to be used in 
3 irrigations. At this rate a Dakota well would pay its 
cost in two years, if not in one. In other states the annual 
charge per acre foot is about the same, but, inasmuch as the 
crop is a certainty and abundant in amount, this apparently 
high tax is not felt as at all burdensome. 

The Dakota irrigator who would achieve success must 
abandon the false idea, which many farmers entertain, of 
getting someting for nothing. He must put in both money 
and labor, and considerable of each, in order to make a suc- 
cess of irrigation. Nor need he be discouraged; for all the 
advantage is on his side . It will cost less here to secure a 
water right than in almost any other section because a given 
volume may be had for a lesser outlay. 

Again, the Dakota water-right is also a water-power 
which very largely increases its value. It is not subject to 
periodic fluctuations, prior rights of up-stream claimants, 
and such other uncertainties and annoyances as are experi- 
enced under other systems. It is perpetual, is under perfect 
control], may be put to many uses and in all respects has a 
value not possessed by water rights in other sections or un- 
der other systems. 

The cost of reservoirs, ditches, gates, etc., is not a part of 
the water right, but a tax upon the land in its preparation 
for irrigation. In this respect also Dakota has a great ad- 
vantage, for her gently rolling or nearly level lands require 
but little preparation as compared with the heavy work of 
terracing, checking, diking, ditching, leveling and otherwise 
treating the land, as so often necessary elsewhere. 

Finally, as to the ANNUAL COST of water. Where, in 
other states, the annual cost is from 25 cents to $5 per acre 
—averaging over $1 — the Dakota average will be but a few 
cents, and in most cases nothing, for the flow of the well be- 
ing continuous, requires no attention or expense. Once ob- 
tained its volume comes free. 

In every essential particular wherein an irrigation system 
burdens the irrigator with expense— first cost of water, an- 
nual cost of water, preparation of ground, future mainte- 
nance of plant— he who irrigates in Dakota bears the least 
burden; has the greatest advantage; the most valuable, con- 
trollable, and diverse right; to say nothing of the proximity 
to the best and largest markets. 



139 

A consideration of many details only tends to strengthen 
and confirm this conclusion that Dakota's artesian irriga- 
tion system will be the cheapest and the best of the many 
systems developed in this country. 

The experience of the failure years, 1888-1889-1890, taken 
in connection with the results obtained by the great crop of 
1891 (See table No. 43 and remarks in connection therewith) 
prove not only the enormous value of water in Dakota but 
substantiate the estimate of duty of water given in table 
16. If the estimate there given is approximately correct, 
and the annual value of water be taken to be but $2 per acre 
then from table 16 it will appear that a well of 1350 gallons 
per minute would be worth $1950 per year or fully 40 per 
cent on its cost. This is assumed to be a rental value. 

To the owner the actual value would be the net value of 
all crops raised in excess of the average yield of non-irriga- 
ted lands in Ms neigliborTiood. No reasonable person will 
estimate the probable average yield of irrigated wheat at 
less than 30 bushels per acre, which average would be fully 
18 bushels more than the average without irrigation. As- 
suming a net return of but 50 cents per bushel, this would 
give to the water a value of $9 per acre to the owner; or an 
amount suflicient to pay the full cost of the well together 
with the cost of the land, in one year. 

This is not an exagerated estimated but rather an under- 
estimate as has been demonstrated by actual experience. 

A parallel cannot fairly be drawn between the values 
either of water or of land as between the fruit growing 
lands of California and the grain fields of Dakota; but mak- 
ing all needful allowances for the character of the crops 
raised, and their value per acre, the value of water to our 
grass and grain fields is still actually far beyond the amount 
which even sanguine estimate would give to it. 

A thousand gold mines would not be so valuable to our 
people as are these artesian waters. Hasten, therefore, to 
develope this pent-up wealth which awaits the opportunity 
to flow to the coffers of each enterprising claimant. 

VALUE OF LAND. 

One, in considering the relative values of irrigated and un" 
irrigated lands, may border closely upon the realm of the 
marvelous while yet not transgressing the bounds of cold 
facts, for it is truly marvelous that the worthless deserts of 
the arid west, have, within a few years, been clothed in semi- 
tropical luxuriance through the agency of irrigation, and 
have been raised in value from actual zero to as much as 
$2000 per acre. It is but a few years since California and 
Colorado were known only as great mining states. To-day, 
through the agency of the impounded waters of the moun- 
tain streams, they have been transformed into great agricul- 



140 

tural states; the harvest of the golden fruit and of golden 
grain having long since superseded in value the harvest of 
the golden metal. Where then there were mining camps 
now there are prosperous cities, and where then vice reigned 
supreme, now peace and plenty bless the community. 

Millions of acres of barren, sage-brush or of sand-flecked 
desert, of lava- beds and of sun-parched plains have been re- 
claimed and are to-day the most valuable and productive 
lands on the continent. It is true that the high values of 
flOOO per acre and upward are usually fancy prices, but 
many thousands of acres have ready market values of from 
^50 to $500 per acre. 

Good lands, under water, the ditching and like preparation 
being done, are worth from $50 to $100 per acre, and find a 
ready market at these figures. 

Any piece of property is truly worth such an amount as 
will represent the principal upon which a fair rate of interest 
can be permanently earned. 

If land will produce annually a crop which will yield a net 
income of $10 per acre that land is worth $100 per acre to a 
man who demands a 10 per cent investment; or $200 per 
acre to a man who is content with 5 per cent. Such values, 
and only such, are legitimate. 

The remarkable development of Southern California has 
been due almost solely to irrigation. As an illustration of 
the increase in property values may be cited the statistics 
relative to San Diego Co., which may be taken to represent 
that section of the state. 

Real Estate. hnpromments. 

1880 1890 1880 1890 

$1,307,302 $20,000,085 $341,948 $4,450,286 

While no corresponding increase can be expected in any 
Dakota county there is still room for an increase in value 
far beyond the present values. Taking Brown Co., S. D., to 
fairly represent the two Dakotas, the average market value 
of the lands of the county would probably not exceed $6 per 
acre. An increase of $5 per acre would add over $6,000,000 
to the valuation of the county and still leave the lands far 
below their actual value. 

Such a change in the ready market value of these lands 
may be brought about within two years if, within that time 
it can be shown that these lands can be made to produce 
from 25 to 50 bushels of wheat to the acre, no matter what 
the season may be. 

^0 doubt exists as to this being demonstrated— it has been 
already in Brown Co. and in other counties within the arte- 
sian basin. 

As soon as the foreign land purchaser and investor learns 
of the wonderful possibilities of this artesian basin the pre- 
sent land owners will find a ready market for their surplus 



141 

holdings at prices now beyond their fairest fancies. What 
is it that can do this magic act— the creation of millions of 
value where now little appears ? What is it that can and 
will do for Dakota what irrigation has done for our sister 
states ? What is it that can banish poverty, misfortune and 
ruin from our state and bring riches, prosperity and happi- 
ness in their place? That can quench the thirst of our 
once parched prairies with a perennial draught of nature's 
purest waters ? 

ARTESIAX WELLS! 

1^0 agency is so pregnant of promise for the welfare of the 
Dakotas and none deserves the same attention as the de- 
velopment of this great industry— artesian irrigation. It is 
not only a boon to him who puts it to practice but to the 
community in which he lives, for it shows to the world the 
possibilities awaiting all who choose to engage therein, and 
fixes to our lands a value because of their latent possibilities 
for successful agrietiltural development. 

The author has heard it remarked, but recently, by a 
wealthy eastern man who owns (perforce) several thousand 
acres of Dakota lands, but possesses no knowledge of irriga- 
tion, that if artesian irrigation proves to be what it is claim- 
ed to be he would sink several wells and thus trebble the value 
of the lands which today he would sell for what they cost. 

No doubt there are scores of such cases, and it is to prove 
to such men the true value of their lands, and to still further 
interest them and their monied friends in schemes of devel- 
opment that every effort should be put forth to demonstrate 
to the world the true extent and value of the latent possi- 
bilities we have within our reach and control . 

Every possible publicity should be given to every truth, 
to every demonstrated fact touching upon the well or irri- 
gation interests, and, by reason of the approaching World's 
Pair and its resultant era of prosperity and commercial 
activity every possible effort should be made to push the 
business of irrigation at home and a knowledge of its results 
abroad; for no better time will ever come for Dakota to 
enthrone herself in the good will of the capitalists of the 
world and regain her lost prestige, than the immediate 
future. 

The farmers and the business men of the state should 
organize and prepare in every legitimate way to promote 
this all important industry, for the success or failure of the 
state depends upon it, and all other interests pale before it 
in importance and the effect upon the general prosperity of 
all classes. If this appeal to the patriotic home enterprise 
of Dakotans shall result in creating any of that interest 
which the subject warrants, then will this little volume not 
have been issued in vain. 



142 
8IZES or FARMS. 

A word of caution as to over-irrigation, in point of area, 
will well-nigh be wasted inasmuch as the invariable tendency 
is to attempt to irrigate too large an area. A few unsuccess- 
ful attempts to irrigate too broad an area will convince the 
farmer that a lesser area, better served and cultivated, will 
yield better results. 

In a fruit-growing country an area of 5 or 10 acres is 
enough for a single holding. As the crop is changed to 
vegetables, grass, or cereals the area which may be advan- 
tageously cultivated increases. It is assumed that the hold- 
ing is worked on the plan of the average farm— by the 
farmer and his family, with the assistance of the average 
amount of hired help. As the number of hands, actively 
engaged in the farm labor, increases, so may the area treated 
be increased. The character of the land to be cultivated— 
whether it be easily managed or the reverse — will likewise 
determine the area which a given service of labor can prop- 
erly manage; as will also, the character of the crops raised. 

It will be well in starting out to thoroughly treat such an 
area as the supply of water,as well as of labor, can treat to the 
best advantage. In short, go only so far as you can go with 
thoroughness. The following year this area will require far 
less attention so tlie surplus of water and of labor may be 
expended in an extension of the area served, until the max- 
imum shall have been reached. No other method of pro- 
ceedure will prove satisfactory unless "bonanza" methods 
are adopted. Table N'o. 53, of statistics, in the 

3d, 4th, 5th and 6th lines, shows at a glance the results 
reached in 7 other states as to areas under irrigation. 

What there is shown is true of all other states and coun- 
tries, except that, as the country becomes older, and irriga- 
tion methods are improved, the duty of water increased, 
and more care and labor is given to a given area, the 
product of that area increases and a lesser holding is relied 
upon. So it will be in Dakota after the irrigation system is 
more general; the farms, instead of becoming larger will 
become smaller, and better and more thorough methods of 
cultivation will be practiced. From these smaller areas 
will be returned a larger yield and one as certain as the 
order of the seasons and as bounteous as the prosperity 
which will attend them. 

" Bonanza " farms may be, and no doubt are, fine things 
for their owners, but they are of little use to any community. 
A community of small farms, all of which are prosperous 
and each of which supports in plenty a family, is the most 
truly a model in all the elements which enter into the gen- 
eral prosperity, wellfare and happiness of the people. So 
each farmer will do better by his own interests, and those 
of his neighbors, if he seeks to place his present holding 
under more thorough cultivation rather than to extend his 
holding and neglect the proper cultivation of the whole. 



143 



PHOTOGRAPHS. 

Any good engraver can engrave a picture of an artesian 
well, and — so to speak— can doctor it up to show according 
to his own ideas of magnitude, or those of the person for 
whom he works, which ideas may far exceed the facts . 

Not so, however, with a photograph or any picture having 
a photograph as iis base — such as photo-engravings. The 
camera, with the quickness of light, makes a record true to 
nature, and of the smallest details; a record with which the 
enthusiast cannot tamper ; which none can question. 

The importance of photographing the wells of the state 
has but recently impressed itself upon the leading photog- 
raphers. Already several of them have quite fine collections 
of views of the wells in their neighborhood ai;d take pains 
to secure views of each new well. Some have made a con- 
siderable profit out of their views, for a fine view finds a 
ready sale at home and abroad. Ere long the sale of well 
views will form an important item in the income of Dakota 
artists. A photograph of a well needs no argument back of 
it; it tells its own story; is its own best witness as to its 
truthfulness to nature, and convices the skeptic who would 
not otherwise accept the facts, as shown, on the affidavit of 
a friend, without some misgivings. 

Hence the importance of taking photographs and giving 
them a wide circulation. They are unimpeachable witnesses 
as to the volume and power of our wells and will command 
respectful attention where the most glowing verbal descrip- 
tion will be wasted on skeptical ears. 

The eastern man who has never seen a flowing well cannot 
comprehend the nature of one from a mere verbal descrip- 
tion; and even an old well driller, unacquainted with such 
great wells, will laugh in his sleeve at the narrator or will, 
with his friend the capitalist, say "that is the biggest 
Dakota lie I have heard yet." 

Show him a photograph, however, and his skepticism 
turns to wonder and amazement. No argument will prevail 
against the evidence of the light, and the capitalist whose 
interest, perchance, has been solicited will turn to investi- 
gate or to invest instead of turning away in disgust or in 
wonder at the stupendous lying abilities of the Dakota man. 

Enthusiasm on the well subject is ligitmate and laudable 
and increases as one sees and learns more of this wonderful 
power and supply. Enthusiasm is still further heightened 
by a comparison of the Dakota wells with those of other 
sections of the country. Not a comparison of reports, set 
in cold type, but a comparison of lifelike photographs. 
It is this enthusiasm that should be fostered by every resi- 
dent of Dakota, and especially by every photographer. 



144 

Every person and corporation should lend every possible aid 
to the photographer in his effort to secure good views; and 
the photographer in his turn should improve every oppor- 
tunity to secure views, and then place them at a price such 
as will enable every one to secure a supply to send away. 

There is no telling what one will And its way into the 
hands of some man who will invest thousands of dollars in 
wells and irrigation projects as the direct result of having 
seen, and been impressed with, a photograph of a well. 
Every person engaged in placing irrigation bonds, or the 
stocks of irrigation companies, should have a collection of 
the bes I views in the state and every eastern bond-negotia- 
ting agent should be similarly supplied. 

Collections of well views could, to excellent advantage, be 
handsomely framed and placed in the lobbies of the leading 
eastern hotels and in other places of popular resort. Such 
exhibitions would be seen by thousands of wondering 
and admiring spectators. Thus would a knowledge of the 
vast possibilities of Dakota's great wells be spread among 
a class of people who could not be reached by other means. 

Thousands of views could in this, and in other ways, be 
placed where they would be a greater advertisement to the 
state at large than any other that could be made. 

A lithograph of a goddess, of an eagle, of a gapping crowd 
of emigrants, or of a chariot procession may be a work of 
art but it can be of little value to the people; but if an equal 
number of views of our great artesian wells were scattered 
over the laud the result would be a large influx of people, 
seeking to share the undoubted benefits the artesian waters 
will confer, and of money to develop an industry upon 
which the agricultural success of this agricultural state 
depends. Every view sent out should have attached a full 
and ACCURATE description covering as many as possible 
of the following points: 

Name, or location of the well. 

When drilled, and by whom. 

Depth, in feet. 

Pipe, size in inches all the way, or at top and at bottom. 

Volume, discharge in gallons per minute when opened 
and full size, and if possible, when discharging 
through smaller sized openings. 

Pressure, in pounds per sq. inch, when closed, and, if 
possible, when streams of different sizes are 
being discharged. 

Discharge, height of throw or discharge of streams of 
different sizes, or the horizontal distance to 
which the streams are thrown. 

Temperature, 
Character of water, hard, soft, clear, muddy, palatable, «fco. 

Use to which the supply is put. 



145 

If several views are had of one well note which view is 
shown and what it is— whether it is the 4 inch stream or the 
6 inch stream, &c. 

Without this description the view has little value, and the 
value even then rests largely on the exact TKUTHFUL- 
XESS of the description given. It is poor policy, to say the 
least, to exaggerate as to^the volume, pressure, discharge, or 
the size or height of the stream shown. 

If an exceptionally line negative is secured a duplicate 
should be made, for some accident may befall the first one 
or it may become gradually worn out through use. 

The author was desirous of having, as a prominent feat- 
ure of this little volume, a series of photogravure views of 
the leading wells of the state but the expense would have 
been greater than the circumstances of its issue would per- 
mit, so the idea was abandoned for the present edition . 
Should the book meet with such favor as to warrant another 
edition this feature will be added thereto. Through the 
courtesy of the leading photographers of the state the author 
has secured a collection of all the views of the wells thus far 
photographed. 

A list is added(on the next page)of the photographers hav- 
ing views, their addresses, and a list of the views they have 
for sale. This will be a great boon to the general public 
who will thus be informed as to what views may be had, and 
where to secure them. By this means it is to be hoped a 
large trade in views may be worked up and the photograph- 
ers thereby stimulated to the work of taking all such views 
as may be possible within their territory. The importance 
of cultivating this mutual interest is far reaching and it is 
hoped that added interest will be taken in well photography 
because of the great good that may flow therefrom to the 
people of all parts or the state. 



The author with pleasure acknowledges the courtesy of 
views received from the following: 
S. W. Fergusson, Bakersfield, Cal. 5 Kern Co. wells. 
Wm. Kennish, Wilmington, N. C. Ponce de Leon well, Fla. 
H. C. Humphrey. North Yakima, Wash. Yakima wells. 
And from all the photographers listed on page 146. 



146 



WHERE TO BUY WELL PHOTOGRAPHS. 



Photographs of Dakota's famous artesian wells may be 
secured by writing to the following Photographers. 



Photographer. 


Address. 


List of Views. 


Grade. 


B. W. Burnett. 


TyndaU, 


Springfield well, 6 inch stream. 


A 




S. D. 


u u ^ u a 


A 


These views 




" and miU. 


A 


are among 




Niobrara, Neb. well^ 8 in. stream. 


A 


the best in 




" " " 2 derrick v'ws 


B 


the state. 




Zinnert well 3 in. stream. 


A 






" " Shadeland farm 


A 


D. 0. Root. 


Woonsocket, 


Large, of City well, 4 in. stream. 


A 




S. D. 


2 small" " 


A 


City well 




Hinds well, vertical stream. 


B 


views are the 




•' " horizontal & vert. s. 


B 


best i n the 








state. 








L. Janousek. 


Yankton, 


Brick yard well, stand-pipe view. 


A 




S. D. 


'■ " " boiler view. 


A 


P. C. Anderson 


Redfleld, 

S. D. 


Water works display view. 


B 


Quiggle & 


Rapid City, 


Doland well 6 inch stream. 


A 


Johnson . 


S. D. 


" 6 " 


A 


J. Q. MiUer. 


Aberdeen, 


Railway well. 


B 




S. D. 


Beard " 6 inch stream. 


A 






" 4 " 


A 






Williams " 4 " 


B 


Chas. H. 


Huron, 


Day well, vertical stream. 


A 


Newcombe. 


S. D. 


" double 


A 






City " water works display. 


A 






10 views of irrigated farm. 


B 


These views 




Risdon well, 8 in. derrick view. 


A 


are also very 




u it ^ u (I a 


A 


nice. 




" " 2 " " "■ 


A 






" 6 " clear 


A 






c. a c a a n 


A 






a (1 A a '« '( 


A 






(1 " ' 2jT " " " 


A 






Kerr " 3 views. 


A 



Note: In the above list A and B refer to the grade or rel- 
ative values of the views. A indicates a view of special ex- 
cellence or interest and B a view of lesser value. 



147 
EXPLANATION OFTABLE OFTANGENTS & COTANG'S-Pl^S 

I. Required the tangent of the angle 65' 20' f 

In the first column of degrees find 65, then pass horizont- 
ally across to the column headed 20' where find 2.17749 as the 
tang, required. If the number of minutes in the given 
angle is not found in the head of the table proceed as 
follows: 

II. Required the tangent of the angle 65' 26 ' f 

Proceed as before to get the tangent for 65" 20', which is 
the next lowest number of minutes given at the head of the 
table. This leaves an excess of 6 minutes. At the right 
hand of the table under the head of ' Prop. (Proportional) 
parts to 1 " find J 69 in the same line with 65' at the left 
side. 169 x 6=1014 which added to 2.17749, the tang, for 65° 
20', equals 2.18763 as the required tangent. {This gives a suffi- 
ciently approximate Tangent for ordinary iise. Exact Tangent =2. 187 55 .) 
COT A N G E NTS are taken from the table by taking the degrees from 
the column of degrees at the right side and the minutes from those indi- 
cated at the foot of the table, thus- 
Ill. Required the cotangent of the angle 24-, 40' ? 

In the right hand column of degrees find 24% then pass 
horizontally across the table— to the left— to column having 
40' at the foot, and find 2.17749 as the cotang. required. 
From this it is seen that the tang, of any angle is the cotang. 
of the complement of that angle, for 65= 20'+24= 40' =90°. 
Proceeding as at II— 

IV. Required the cotangent of angle 24° 34' f 
(The complement of 65" 26'.) 

Obtain cotangt. for 24" 30' which=2.19430 and from col- 
umn of prop, parts find 169, which multiplied by 4, for the 
4' we have in excess of 30 ',=676. Where, in finding the 
tangent, this correction was added it is now subtracted, in 
finding the cotangent. 2.19430 minus 676=2.18754 
The exact cotang ent = 2.18755. 

USE OF TABLE OF TANGENTS- 

Tangents are used principally in determining heights and distances by 
means of angles. Refering to Fig. 11. page 93, suppose a surveyor's tran- 
sit to be set at A, so the angle FAE can be measured, and suppose that 
angle to be 38° 40 . The line EF is the tangent of the angle FAE. From 
the table we find the tangent of the angle 38° 40 to be .80020 which mrd- 
tiplied by 100, the distance from A to F, =80.02 or 80 ft. as the height of the 
stream. 

Proceed in like manner, for any other angle, to multiply the horizontal 
distance by the tabular tangent to get the length of the tangent. Suppose 
a 2 ft. ride is used to measure the angle, as described on page 158, and 
that the opening of the rule is 8 inches— which cor- 
^|l<?'. responds to an angle of 38° 57— and that the joint 

is 100 feet from the well. We find from the follow- 
ing table that the tang, for 38° 57 =.80855 whichXlOO 
= 80.85. In this simple way the height of a stream 
may be determined within a foot or less. 

So, too, in measuring horizontal distances to in- 
accessible points, as across a stream. Suppose it 
is desired to measure the distance A B, Fig. 24, be- 
tween points on opposite sides of a river, across 
which measurements cannot be carried. From A 
lay off a right angle BAC and measure A C any 
suitable length, say 350 feet. From C measure an- 
gle A C B which=60° 5 —then tang, of 60° 5' = 
Fig 24 1.7.?805which X350=608.3 ft , the distance from A to B 




148 
TABLE NO. 78. 

See explanation of table on page 147. 
NATURAL TANGENTS. 





















Prop 


Deg. 


0' 


10' 


20' 


30' 


40' 


50' 
01455 




Deg. 


parts 
tol' 





00000 


00291 


00582 


00873 


01164 


01746 


89 


29 


1 


01746 


02036 


02328 


02619 


02910 


0.3201 


03492 


88 


29 


2 


03492 


oifim 


04075 


04366 


046.58 


04949 


05241 


87 


29 


3 


05241 


0553:3 


0.5824 


06116 


06408 


06700 


06993 


86 J 


29 


4 


06993 


07285 


07578 


07870 


08163 


08456 


08749 


85 


• 29 


5 


08749 


09042 


09335 


09629 


09923 


10216 


10510 


84 


29 


6 


10510 


10805 


11099 


11394 


11688 


11983 


12278 


83 


29 


7 


12278 


12574 


12869 


13165 


13461 


1.37.58 


14054 


82 


30 


8 


14054 


14351 


14648 


14945 


1.5243 


1.5540 


1.5838 


81 


30 


9 


15838 


16137 


16435 


16734 


17033 


17333 


176.33 


80 


30 


10 


1763:^ 


179.33 


18233 


18534 


18835 


19136 


19438 


79 


30 


11 


19438 


19740 


20042 


20345 


20648 


209.52 


21256 


78 


30 


12 


21^6 


21560 


21864 


22169 


22475 


22781 


23087 


77 


31 


13 


23087 


23:393 


23700 


21008 


24316 


24624 


249,33 


76 


31 


14 


249^33 


25242 


25552 


25862 


26172 


26483 


26795 


75 


31 


15 


26795 


27107 


27419 


277:32 


28046 


28360 


2S675 


74 


31 


16 


28675 


28990 


2930.5 


29621 


299.38 


30255 


30573 


73 


32 


17 


30573 


30891 


31210 


31530 


31850 


.32171 


32492 


72 


32 


IS 


32492 


32814 


33136 


33460 


.33783 


34108 


34433 


71 


32 


19 


344a3 


3475S 


35085 


a5412 


35740 


36068 


36:397 


70 


33 


20 


36397 


.36727 


37057 


37388 


37720 


38053 


38386 


69 


33 
34 
34 


21 


38386 


38721 


390.55 


39391 


39727 


40065 


40403 


68 


22 


40403 


40741 


41081 


41421 


41763 


42105 


42447 


67 


23 


42447 


42791 


43136 


43481 


43828 


44175 


44.52:3 


66 


34 


24 


44523 


44872 


45222 


45573 


45924 


46277 


46631 


65 


35 


25 


46631 


4698.5 


47341 


47698 


48055 


48414 


48773 


64 


36 


; 26 


48773 


49134 


49495 


498.58 


50222 


50.587 


509.53 


63 


36 


! 27 


.509.53 


.51319 


51688 


52057 


.52427 


.52798 


53171 


62 


37 


! 28 


53171 


,53545 


53920 


54296 


54673 


5.5051 


5.5431 


61 


38 


■ 29 


5.5431 


55812 


56194 


56.577 


56962 


57348 


577S5 


60 


38 


80 


57735 


58124 


.58513 


58905 


59297 


.59691 


60086 


.59 


39 
40 
41 


i '^1 


60086 


60483 


60881 


61280 


61681 


62G83 


62487 


58 


32 


62t87 


62892 


63299 


6.3707 


64117 


61.528 


64941 


57 


! 33 


64941 


6.5355 


6.5771 


66189 


66608 


67028 


67451 


.56 


42 


34 


67451 


67875 


68301 


68728 


691.57 


69.588 


70021 


55 


43 


35 


70021 


7045.5 


70891 


71329 


71769 


72211 


726.54 


54 


44 
45 
46 
47 


36 


726.54 


73100 


7.3547 


73996 


74447 


lidOO 


7.>3>5 


53 


37 


75355 


75812 


76272 


76733 


77196 


77661 


78129 


.52 


38 


78129 


78598 


79070 


79544 


80020 


8049S 


80978 


51 


39 


80978 


81461 


81946 


82434 


82923 


8.3415 


83910 


50 


49 


40 


83910 


84407 


84906 


85408 


8.5912 


86419 


86929 


40 


50 
52 
53 
55 
57 


41 


86929 


87441 


8795.5 


88473 


88992 


89515 


90040 


48 


42 


90040 


9a569 


91099 


91633 


92170 


92709 


93252 


47 


43 


93252 


93797 


94345 


94896 


95451 


96008 


96.569 


46 


44 


96569 


97133 


97700 


98270 


98843 


99420 


1.00000 


45 


Deg. 




50' 


40' 


30' 


20' 


10' 


0' 


Deg. 





NATURAL COtANGENTS. 



149 
TABLE NO. 79 -Contimied. 



NATURAL TANGENTS. 





















Prop 


Deg. 


0' 


10' 


20' 


30' 


40' 


50' 




Deg. 


parts 








1.01170 


1.01761 


1.0235.5 


1.02952 






tol' 


45 


1,00000 


1.00583 


1.0:355:3 


44 


59 


46 


1.03553 


1.04158 


1.04766 


1.05378 


1.05994 


1.06613 


1.07237 


4S 


61 


47 


1.072:37 


1.07864 


1.08496 


1.091:31 


1.09770 


1.10HU4 


I.1I061 


42 


63 


48 


1.11061 


1.11713 


1.12:369 


1.13029 


1.1:^694 


1.14.363 


l.l.5a37 


41 


66 


49 


1.15037 


1.16715 


1.16398 


1.17085 


1.17777 


1.18474 


1.19175 


40 


69 


.50 


1.19175 


1.19882 


1.20593 


1.21310 


1.22031 


1.22758 


1.2.3490 


39 


72 


51 


1.23190 


1.24227 


1.24969 


1.2.5717 


1.26471 


1.272:30 


1.27994 


as 


75 


52 


1.27994 


1.28764 


1.29541 


1.30323 


1.31110 


1 31904 


l.:3-704 


37 


78 


5:^ 


1.32704 


1. 3^511 


1.34323 


1.35142 


135968 


1 36800 


l.:376.')8 


36 


82 


54 


1.376;i8 


1.38484 


1.39336 


1.40195 


1.41061 


1.41934 


1.42815 


S5 


86 


55 


1.42815 


1.43703 


1.44598 


1.45501 


1.46411 


1.47330 


1.48256 


34 


90 


56 


1.48256 


1.49190 


). 50133 


1..510.S4 


1.52043 


1.5:3010 


1.6.3987 


:33 


95 


57 


1.539S7 


1.51972 


1.55966 


1.56969 


1.. 57981 


1 .59002 


1.600:38 


32 


100 


.58 


160033 


1.61074 


J. 6212.5 


1.63185 


1.64256 


1.65a37 


1.66428 


31 


107 


59 


1.66428 


1.67530 


1.68643 


1.69766 


1.70901 


1.72047 


1.73205 


30 


113 


60 


1.73205 


1.74375 


1.75556 


1.76749 


1.77955 


1.79174 


1.80405 


29 


120 


61 


1.80405 


1.81649 


1.82906 


1.84177 


1.85462 


1.86760 


1.88073 


'M 


128 


62 


1.88073 


1.89400 


1.90741 


1.92098 


1.93470 


1948.58 


1.96261 


9; 


136 


m 


1.96261 


1.97680 


1.99116 


2.00569 


2.020:39 


2.03526 


2.05030 


L"C 


146 


64 


2.05030 


2.06553 


2.08094 


2.09654 


2.11233 


2.12832 


2.14451 


1:5 


157 


ft5 


2.14451 


2.16090 


2.17749 


2.19430 


2.21132 


2.22857 


2.24604 


24 


169 


66 


2.24604 


2.26374 


2.28167 


2.29984 


2 31826 


2.:33693 


2.35585 


23 


183 


"57 


2.3.S585 


2.37.504 


2.39449 


2.41421 


2.434-'2 


2.45451 


2.47509 


22 


199 


68 


2.47509 


2.49597 


2,51715 


2..53865 


2.56046 


2.58261 


2.60509 


21 


217 


69 


2.60509 


2.62791 


2.65109 


2.67462 


2.69853 


2.72281 


2.74748 


20 


235 


70 


2.74748 


2.77254 


2.79802 


2.82391 


2.85023 


2,87700 


2.90421 


19 


261 


71 


2.90421 


2.93189 


2.96004 


2.98868 


3.01783 


3.04749 


3.07768 


18 


289 


72 


3.07768 i 3.10842 


3.13972 


3.17159 


3.20406 


3.23714 


3.27085 


17 


322 


73 


3.27085 ! 3.30521 


3.34023 


3.;37594 


3.41236 


3.44951 


3.48741 


16 


360 


74 


3.48741 


3.52609 


3.56557 


3.60588 


3.64705 


3.68909 


3,73205 


15 


407 


75 


3.73205 


3.77595 


3.82083 


3.86671 


3.91364 


3.96165 


4.01078 


14 


464 


76 


4.01078 


4.06107 


4.11256 


4.16530 


4.21933 


4.27471 


4.33148 


13 


534 I 


77 


4.33148 


4.38969 


4.44942 


4.51071 


4.57363 


4.63825 


4.70463 


12 


621 i 


78 


4.70463 


4.77286 


4.84.300 


4.91516 


4.98940 


5.06584 


.5.144.55 


11 


732 ! 


79 


5.14455 


5.22566 


5.30928 


5.39552 


5.48451 


5.57638 


6.671-J8 


10 


876 


80 


5.67128 


5.76937 


5.87080 


5.97576 


6.08444 


6.19703 


6.31375 


9 


1068 


81 


631375 


6.48481 


6.56055 


6.69116 


6.82694 


6.96823 


7.11.5:37 


8 


1331 


82 


7.11537 


7.26873 


7.42871 


7.59.575 


7.77035 


7 95302 


8-14435 


7 


1708 i 


83 


8.1443.5 


8.34496 


8.55S55 


8.77689 


9.009S3 


9.2.55:30 


9.514-36 


6 


2270 i 


84 


9.51436 


9.78817 


10.0780 


10.3854 


10.7119 


11.0594 


11.4.301 


5 


3168 


85 


11.4301 


11.8262 


12.2.505 


12.7062 


1.3.1969 


13.7267 


14.3007 


4 


4728 


86 


14.3007 


14.9244 


15.6048 


16.3499 


17.1693 


18.07.50 


lO.ObU 


3 


7806 


87 


19.0811 


20.2056 


21.4704 


22.90.38 


24.5418 


26.4316 


28 636:3 


2 




88 


28.6363 


31.2416 


34.3678 


.38.1885 


42.9641 


49.10.39 


.57.2900 


1 




89 


57.2900 


68.7501 

50' 


85.9.S98 
40' 


114.589 


17.1.885 


343 774 


«' 







Beg. 


.30' 


20' 


10' 


Deg 



. NATURAL COTANGENT.S. 



150 

MENSURATION. 
WEIGHTS, MEASUKES A:N^D USEFUL NUMBEES. 

AVOIRDUPOIS OR COM M ERCIAL WEIGHT. 

^ 16 drachms = 1 ounce = 437.5 grains. 

16 ounces = 1 pound = 256 drachms = 7000 grains. 
28 pounds = 1 quarter = 448 ounces. 
4 quarters = 1 cwt. = 112 pounds. 
20 cwts. = 1 ton = 2240 pounds (long ton.) 
2000 pounds = 1 short or commercial ton. 

APOTHECARIES WEIGHT. 

20 grains = 1 scruple. 

3 scruples = 1 drachm = 60 grains. 

8 drachms = 1 ounce = 480 "' = 24 scru. 

12 ounces = 1 pound = 5760 " = 288 " = 96 drms. 

LONG MEASURE. 

12 inches = 1 foot. 



3 feet 


= 1 yard 


= 36 inches. 




161/2 " 


= Irod 


= 198 " 




160 rods 


= Y2 mile 


= 31680 " 


= 2640 feet. 


320 " 


= Imile 


= 63360 " 


= 5280 " 


3 miles 


= 1 league 






A palm = 


3 ins. A hand = 4 ins. A 


span = 9 ins 


A fathom 


= 6 ft. 







GUNTERS CHAIN. 

7.92 inches = 1 link. 
100 links = 1 chain = 4 rods = 22 yards = 66 feet. 
80 chains =^ 1 mUe = 320 "' = 1760 " = 5280 " 

SQUARE MEASURE. 



144 square 


s inches 


= 1 square foot. 


9 


feet 


= 1 • 


yard. 


100 


" 


= 1 ' 


(architects measure.) 


30.25 " 


yards 


= 1 ' 


rod. 


160 


rods 


= 1 ' 


acre. 


16 


(( 


= 1 ' 


chain. 


10 


chains 


= 1 ' 


acre. 


640 


acres 


= 1 ' 


mile. 


43,560 sq. ft. = 1 acre = 208. 


71 ft. on each side. 


A circular 


acre i? 235.504 ft. 


in diameter. 



MEASURES OF VOLUMES. 

LIQUID MEASURE. 

{See also Page 151.) 

4 gills = 1 pint = 16 ounces. 
2 pints = 1 quart = 8 gills = 32 ounces. 
4 quarts = 1 gallon = 32 " =8 quarts. 
31i gallons = 1 wine barrel. 
63 '• =1 hogshead. 

DRY MEASURE. 

2 pints = 1 quart. 

4 quarts = 1 gallon = 8 pints . 

2 gallons = 1 peck = 16 " =8 quarts. 

4 pecks = 1 bushel = 64 " =32 " =8 gallons 



151 
MENSURATIOX, continued. 



CUBIC MEASURE. 

1728 cubic inches = 1 cubic foot. 
27 " feet = 1 " yard = 46,656 cu. in. 
Note— A cubic foot contains 2200 cylindrical ins., 3300 spherical Ins., or 
6600 conical inches. 

LIQUID MEASURES. 

Giving approximate sizes of measures to contain given quantities of 
liquid. 





Diam. ins. 


Height. 




Diam. ins. 


Height. 


Gill 


1% 


3 


Gallon 


7 


6 


Half pint 


•IM 


3% . 


2 gallons 


7 


12 


Pint 


31/2 


3 


8 


14 


12 


Quart 


31/2 


6 


10 


14 


15 



A cylinder 1 ft. in diameter and 1 ft. high contains 

.02909 cubic yards. 1 2.524 U. S. dry pecks. 

.7854 " feet. 20.196 U. S. dry quarts. 

1357.1712 " inches. | 40.392 U. S. dry pints. 

.6311 U. S. dry bushels. \ 23.50 US. liquid quarts. 

5.876 U. S. gallons ^ 48.96 lbs. 



SQUARE BOX MEASURE. 

A box 24 X 16 inches square and 2S inches deep contains a barrel. 

24 X 16 " •' 

16 X 16% " 

12 X 1U4 " 

SH X %\i " 

814 X 8f4 " 

314 X 4% " 

4 X 414 " 



14 " 


" 'A ■ " 
1 bushel. 

" 1/ " 


(5 

8 •' 
4 " 
4 " 
4 ■• 


72 

" Ipeck. 
1 gaUon. 

" 1/2 " 
1 quart. 



MISCELLANEOUS 

A CUBIC FOOT is Equal to 

1728 cubic inches. 

.037037 cubic yard. 

7.48052 liquid gallons (of 231 cu. ins.) 

6.42S51 U. S. dry gaUons. 

.803564 U. S. bushels (of 2150.42 cu. in.) 

3.31426 U. S. pecks. 

3:300.23 spherical inches. 

.23748 U. S. liquid barrel of 31!.^ gals. 

62.425 pounds of pure water (approximately 62^3 lbs.) 

A CUBIC YARD is Equal to 

27 cubic feet. 

46,656 cubic inches. 

21.69623 U. S. bushels (struck.) 

201.974 U. S. gaUons. 

A GALLON is Equal to 

231 cubic inches. 

8.3216 pounds of water (by some authorities 8.3388) 8M lbs. 

.13'36S cubic foot. 

A cylinder 7 inches in diam. and 6 inches high. 

A cube 6.13.58 inches on a side. 



152 
MEN^UKATION, continued. 

OF SQUARES, RECTANGLES AND CUBES. 

The area of any parallelogram = length X width. 
Area of square = square of one side. 

The side of a square equal ? _ 5 diameter X .88623, or 
in area to a given circle ) I circumference X .2821. 

To find side of inscribed square X diameter by .7071. 

Area of inscribed square = square of radius X 2. 

The side of a square X 1 .128 = diameter of an equal circle. 

Side of square = square root of its area. 

Side of square = square root of Vz the square of the diagonal. 

The side of a square =the diagonal X .707107 or -^ 1.4:1421 

Side of square X 1.51967= side of equilateral triangle of equal area. 

The diagonal = the sq. root of twice the square of a side. 

The diagonal = side X 1.41421 

The length of a rectangle = area ^ breadth. 

The 4 angles of any quadrilateral = 4 right angles. 

Any two adjacent angles of any parallelogram = 2 right angles. 

The contents of a cube = length X breadth X height. 

The length of the side of a cube = the cube root of its contents. 

OF TRIANGLES AND POLYGONS. 

The area of any triangle = * ^f^^^^^^ f^fbtl'."' 

mi^ u .4 41 _ i half the product of the 2 sides and 

i the natural sine of the contained an^le. 

The complement of an angle = its defect from a right angle (90°) 

" supplement " " = " " " two right angles (180°) 
The 3 angles of any triangle = 2 right angles. 
Area of trapezoid = altitude X Yz the sum of the parallel sides. 
Area of trapezium = divide into 2 triangles and and find their area. 
Area of equilateral triangle — square of a side X .433. 

( sum of its sides X perpendicular 
Area of any regular polygon = •] from center to one side and product 

( divided by 2. 

OF CIRCLES. 

DIAMETER X 3.14159 = circumference. (commonly, 3.1416) 
" X .88623 = side of equal square. 

" X .7071 = " '• inscribed square. 

" squared X .7854 = area of circle. 

" = circumference -f- 3.14159 (3.1416). 

'' = side of equal square -j- .8S62. 

" = " " inscribed square ^ .7071. 



" = varea -^ .7854. 

" = circumference X 0.3183. 

" = • '* X 7 and product -^ 22. 

" =1.12837 X square root of the area. 

" = as 355 is to 113 so is circumference to diameter. 

CIRCUMFERENCE ^ 3.1416 = diameter. 
'• = diameter X 3.1416. 

'' = 3.5446 X square root of area. 

" = as 113 is to 355 so is diameter to circumference. 

AREA = square of diameter X . 7854. 
" = " " circumference X .07958. 
" = /4 diameter X M circumference. 
" • = square of radius X 3.1416. 

u _ 5 areas of circles are to each other as the squares of their 
~ i diameters. 

Continued on next page. 



153 



MERSURATION, continued. 



Doubling the diameter of a circle increases the area 4 times. 

To find diameter of cicle = 
in area to a given square 



X side of given square by 1.12837. 



Diameter of circle of equal priphery as square = side X 1.2732. 
Side of square of equal periphery as circle = diameter X .7854. 

Diameter X 1.3468 = side of an equilateral triangle of equal area. 

Length of arc = number of degrees X .017453 X radius. 

f From area of outer circle take the area of 
I inner cicle, remainder — area. 
Area of circular ring = -! or 

1 Sum of diameter X difference of diameters 
Land product X .7854. 

Area of sector of circle — length of arc X Vz radius. 

Surface of cylinder equals circumf . X length + area of two ends. 



area of end X length . 
diameter X circumf. 
cubeofdiam. X .5230. 
area of base X Yz altitude. 

i area of base X }i altitude . 

The square of the diam. of a sphere X 3,1416 = its surface. 
The product of the two axes of an eclipse X .7854 = its area. 
The sq. rt. of Yz the sum of the squares of the two diameters of an 
elipse X 3.1416 = its circumference. 



Contents " 

Surface of sphere 
Contents " 
" of widge 
'* pyramid 



USEFUL MULTIPLIERS. 



Note : The converse is obtained by dividing instead of by multiplying. 



Lineal feet 

yards 
Square inches 
feet 
■' yards 
Acres 
Cubic inches 

" feet 
Circular inches 
Cylindrical inches 

•' feet 
Links 



Feet 

Square feet 
Width in chains 
Cubic feet 

'* inches 
Cylindrical feet 

" inches 

U. S. gallons 
U.S. " 
Cubic feet 
U.S. bushels 
tt)S. avoirdupois 
Cu. ft. water 



7.48052 
.004329 
5.874 
.0034 
.133679 
231. 
.8036 
1.2446 
.00045 
62.425 
,, 62.37925 
268.8 gallons of water = 1 ton. 
35.88 cu. ft. " " =1 " 
A column of water 12 inches high by 



X 
X 
X 
X 
X 
X 
X 
X 
X 
X 
X 
X 
X 
X 
X 
X 
X 
X 
X 
X 
X 
X 
X 
X 
X 
X 
X 



.00019 

.000568 

.00695 

.111 

.0002067 

.4840 

.00058 

.03704 

.00546 

.0004.546 

.02909 

.22 

.66 

1.5151 

2.2957 



miles. 

square feet. 

" yards, 
acres. 

square yards, 
cubic feet. 

" yards, 
square feet, 
cubic '• 

'• yards, 
yards, 
feet, 
links. 

square links, 
acres per mile. 

U. S. gallons. 

(1 (( 



cubic feet. 

" inches. 
U.S. bushels, 
cubic feet, 
tons (2240 lbs.) 
lbs. avoir, 
lbs. (according to Haswell.) 



1 inch diameter = .341 lbs. 



154 
MISCELLANEOUS NOTES. 



CORN AND HOGS. 

A bushel of corn will make lOYz lbs. of pork, gross. Then : 

When corn costs Pork costs 

IZM cents per bushel I14 cents per pound. 

■ ■' ' 2 

3 
4 
5 
6 

Jones dt Laughlin. 



17 




25 




35 




42 




50 





TABLE NO. 54. 

TABLE OF TIME. 



New. 



Time. 


Days. 


Hours. 


Minutes, 


Seconds. 


1 minute 
1 hour 
1 day 


= 








60 
3600 

86 400 • 






60 
1440 




24 


1 week 


^ 


7 


168 


10 080 


604 800 


1 civil month 


1=. 


28 


672 


40 320 


2 419 200 


1 month 


=: 


30 


720 


43 200 


2 592 000 


1 month 


= 


31 


744 


44 640 


2 678 400 


2 months 


= 


60 


1440 


86 400 


5 184 000 


3 " 


=: 


90 


2160 


129 600 


7 776 000 


6 ■' 


= 


180 


4320 


259 200 


15 552 000 


1 year 


= 


365 


8765 


525 948 


31 556 829 


1 year 


= 3( 


55 ds., 5 hrs., 48 min. 


, 49tu sec. 




1 year 


R 


2 weeks, 1 day. 5 h., 
L month of 28 or 29 d 


48 m., 49/0 sec. 
ays (Feb.) 




1 year 


-\ 


t months of SO days. 

? " "31 " 







"A Solar Day is the time between two successive solar noons, or 
transits (passages) of the sun over the meridian of a place. These inter- 
vals are not of equal length all the year around. The average length of 
all the solar days is called the Mean Solar Day; and is the sarae 
as the common civil day of '^4 hours of clock time. Civil noon is 
at 12 o'clock ; but solar, or apparent noon, may be about 14^2 min. before ; 
or I6I4 min. after 12 correct clock time. A Siderial Day is the inter- 
val between two passages of the same star past the range of two fixed ob- 
jects ; and is the precise time required for one complete revolution of the 
earth on its axis. The sideral day never varies ; but is always equal to 23 
hours, 56 minutes, 4.09 sec, so that a star will on any night appear to set, 
or to pass the range of any two fixed objects, 3 min., 55.91 sec. earlier by 
the clock than it did on the night before, so that the number of sideral 
days in a civil year is 1 greater than that of the civil days. 

An Astronomical Day degins at noon, and its hours are counted 
from to 24. In comparing it with the civil day, the last is supposed to 
begin at the midnight before the noon at which the first began." 

Example : Nov. 15 (civil day) begins at midnight; while Nov. 15 (astro- 
nomical day) does not begin untU 12 hours later, i. e. at noon of Nov. 15, 
civil day. 

9 A. M. of civil day = 21 o'clock of artronomical day. 
3 P. M. " *' •' = 3 " " " " 



155 
TABLE NO. 55. 

TABLES OF WAGES. 



WAGES PER HOUR, AT DIFFERENT RATES PER DA\ 


r 






On basis of 10 hours to the day. 




Neil). 


Time. 


Wages per day. 




1.50 


1.75 


2.00 


2.25 
.11 


2.50 


3.00 


4.25 


Vz hour. 


.07 


.08 


.10 


.12 


.15 


.21 


1 


.15 


.17 


.20 


.22 


.25 


.30 


.42 


2 


.30 


.35 


.40 


.45 


.50 


.60 


.85 


3 '* 


.45 


.52 


.60 


.67 


.75 


.90 


1.27 


4 " 


,60 


.70 


.80 


.eo 


1.00 


1.20 


1.70 


5 


.75 


.87 


1.00 


1.12 


1.25 


1.50 


2.12 


6 " 


.90 


1.05 


1.20 


1.25 


1.50 


1.80 


2.55 


7 " 


1.05 


1.22 


1.40 


1.57 


1.75 


2.10 


2.97 


8 " 


1.20 


1.40 


1.60 


1.80 


2.00 


2.40 


3.40 


9 


1.35 


1..57 


1.80 


2.02 


2.25 


2.70 


3.82 


1 D?y 


1.50 


1.75 


2.00 


2.25 


2.50 


3.00 


4.25 


3.00 


3.50 


4.00 


4.50 


5.00 


6.00 


8.50 


3 


4.50 


5.25 


6.00 


6.75 


7.50 


9.00 


12.75 


4 


6.00 


7.00 


8.00 


9.00 


10.00 


12.00 


17.00 


5 


7.50 


8.75 


10.00 


11.25 


12.50 


15.00 


21.25 


6 


9.00 


10.50 


12.00 


13.50 


15.00 


18.00 


25.50 


7 " 


10.50 


12.25 


14. oa 


15.75 


17.50 


21.00 


29.75 


M " 


.38 


.44 


.50 


.56 


.62 


.76 


1.06 


M " 


1.12 


1.31 


1.50 


1.68 


1.87 


2.25 


3.18 



By combination of rates given, amounts per hour at other rates may be 
quickly found. — -amounts at 2.25 + 1.50 equal amount at 3.75 etc. 

WAGES PER DAY, AT DIFFERENT RATES PER MONTH, AND ON 
BASIS OF DIFFERENT NUMBER OF DA\S IN THE MONTH. 



•S 6 


Rate per day, at following rates per month. 




$ 
20 

.77 
.71 
.67 
.65 


25 

.96 

.89 
.83 

.81 


30 

1.15 
1.07 
1.00 

.87 


35 

1.34 
1.25 
1.17 
1.13 


40 

1.54 
1.43 
1.33 
1.29 


45 

1.73 
1.61 
1.50 
1.45 


50 


55 


60 


75 


80 


90 


100 


26 
28 
30 
31 


1.92 
1.79 
1.67 
1.62 


2.12 
1.96 
1.83 

1.78 


2.31 
2.14 
2.00 
1.94 


2.89 
2.67 
2.50 
2.42 


3.08 

2.85 
2.67 

2.58 


3.46 
3.21 
3.00 
2.90 


3.85 
3.57 
3.33 
3.23 



It is the practice among most large mercantile conserns and corpora- 
tions, and railway companies, to pay on the basis of 26 days to the month, 
that being the average number of working days. AU government em- 
ployees are paid on substantially the same basis. 



WAGES PER HOUR 


..AT 


DIFFERENT RATES PER MONTH, AND ON 




BASIS OF 26 DAYS TO THE MONTH. 






Time. 


Rate per hour 


, at following rates per month. 






20 


25 


30 


35 


40 


45 


50 
.19 


60 


75 


90 


1 hour. 


.08 


.10 


.12 


.14 


.15 


.17 


.23 


.28 


.34 


2 hours 


.16 


.19 


.23 


.28 


.31 


.34 


.38 


.46 


.57 


.69 


3 " 


.23 


.29 


.35 


.42 


.46 


.51 


.57 


.69 


.86 


1.03 


4 " 


.31 


.38 


.46 


.55 


.61 


.69 


.76 


.92" 


1.15 


1.38 


5 " 


.39 


.48 


.58 


.69 


.77 


.86 


.96 


1.15 


1.44 


1.73 


6 " 


.46 


.57 


.69 


.82 


.92 


1.03 


1.15 


1.38 


1.72 


2.06 


7 " 


.54 


.67 


.81 


.95 


1.07 


1.21 


1.34 


1.61 


2.01 


2.42 


8 " 


.62 


.76 


.92 


1.08 


1.23 


1.38 


1.53 


1.84 


2.30 


2.76 


9 •' 


.69 


.86 


1.04 


1.21 


1.38 


1.55 


1.72 


2.07 


2.59 


3.11 


1 day. 


.77 


.96 


1.15 


1.34 


1.54 


1.73 


1.92 


2.31 


2.89 


3.46 



156 



AREA OF FIELDS. 

TABLE NO. 56. 

SHOWING SIZES OF A ONE ACRE FIELD, THE WIDTH ADVANCING 

BY 5 FEET. New. 



Wide 


Long 


Wide 


Long 


Wide 


Long 


Wide 


Long 


Wide 


Long 


ft.l 


43560 


45 


968 


90 


484 


135 


322.7 


180 


242 


5 


8712 


50 


971.2 


95 


458.5 


140 


311.1 


185 


235.5 


10 


4356 


55 


792 


100 


435.6 


145 


300.4 


190 


229.3 


15 


2904 


60 


726 


105 


414.9 


150 


290.4 


195 


223.4 


20 


2178 


65 


670.2 


110 


396 


155 


281 


200 


217.8 


25 


1742.5 


70 


622.2 


115 


378.8 


160 


272.3 


205 


212.5 


30 


1452 


75 


580.8 


120 


363 


165 


264 


208.71 


208.71 


35 


1244.6 


80 


544.5 


125 


348.5 


170 


256.3 


II 


40 


1089 


85 


512.4 


130 


335.1 


175 


248.9 


A square acre . 



This table is near enough for all practical purposes. If 
the exact size is required to a second decimal place, or the 
length corresponding to any width not given in the table, 
divide 43,560 (the number of sq. ft. in 1 acre) by the given 
width. Thus: what will be the length of a field of one acre 
the width being 183.7 ft. ? 

43,560^183.7=237.12 ft. long. 

In like manner obtain the area or the size of any rectangu- 
lar field. Had it been desired to find the length of a field of 
17 acres the width of which was to be 183.7 ft. then 43,560 
would be multiplied by 17 and the product divided by the 
given "width. 

If the length and breadth are given and the area is wanted 
divide the total area in square feet (the product of the 
lengthxby the breadth) by 43,560 and the answer will be in 
acres. In the above table the doubling of any 07ie dimen- 
sion doubles the area— 1089 ft. long by 80 ft. wide would 
contain 2 acres; but doubling hotJi dimensions increases the 
area 4 times— 2178 long by 80 ft. wide=4 acres. 



TABLE NO. 57 

SHOWING SQUARE FEET IN DIFFERENT AREAS. 



Nei'J. 



Acres. 


Square feet of area . 


Acres. 


Square feet of area. 


y^ 


21780 


60 


2 613 600 


1 


43 560 


80 


3 484 800 


2 


87 120 


100 


4 356 000 


3 


130 680 


120 


5 227 200 


4 


174 240 


160 


6 969 600 


5 


217 800 


240 


10 454 400 


6 


261 360 


320 


13 939 200 


7 


304 920 


480 


20 908 800 


8 


348 480 


640 


27 878 400 


9 


392 040 


800 


34 848 000 


10 


435 600 


960 


41 817 600 


20 


871200 


1120 


48 787 200 


40 


1 742 400 


1280 


55 756 800 



157 
AREA OF FIELDS, continued. 



1 Acre 


= 10 square chains. 


1 square acre 


= 208.71 feet on a side. 


1 " 1/2 " 


= 147.581 " 


1 " U " 


= 104.355 " 


1 circular " 


= 235.50 " in diameter 


1 " H " 


= 166.52 " " 


1 " M '' 


= 117.75 " " 



AREA OF RAILWAY RIGHT OF WAY. 

50 feet wide contains . 1148 acres to 100 feet of length. 
100 '• " '• .2296 •' " 100 " " 

50 " " •' 6.06 " " 1 mile " 

100 " " " 12.12 '• " 1 " 

If the field is of irregular form divide it up into smaller 
rectangular or triangular pieces, estimate the area of each 
in cu. ft., add these areas and divide the total by 43,560 to 
get the area in acres. The division may be made by platting 
the outline of the field on paper, then making the divisions 
desired, and taking the measurements of the parts from the 
scale of the drawing. 

If the measurement has been made in chains and links 
point off 5 places from the right of the product obtained, to 
get the area. Example.— A field is 8 chains and 20 links 
wide and 10 chains and 45 links long— what is the area in 
acres ? 

8.20x10.45=8.56900. (5 places being pointed off.) Multi- 
ply the 5 figures cut off (.56900 in this case) by 4 and again 
point off 5 figures, the remainder is roods; multiply the 5 
figures cut off by 4 and again cut off 5 figures to get a re- 
mainder in rods or perches. In the above example 56900x4 
=2.27600 and 27600 x4= 1.10400. Therefore, above field 
equals 8 acres, 2 roods andl.103 rods in area. 
TABLE NO. 58. 





NUMBER OF HILLS ON ONE ACRE. 


Haswell. 


Ft. apart 


No. 
43560 


Ft. apart 


No. 


Ft. apart 


No. 


Ft. apart 


No. 


1 


5 


1742 


9 


538 


16 


171 


VA 


19.S60 


51/2 


1440 


91/2 


482 


17 


151 


. 2 


10890 


6 


1210 


10 


435 


18 


135 


2H 


6969 


m 


1031 


101/2 


361 


20 


108 


3 


4840 


7 


889 


12 


302 


25 


69 


314 


3556 


7^2 


775 


13 


258 


.30 


48 


4 


2722 


8 


680 


14 


223 


35 


35 


41/2 


2151 


8H 


692 


15 


193 


40 


27 



PRISMOI DAL FORMULA. 

A prismoid is a solid bounded by six plain surfaces only 
two of which are parallel. 

To find the contents of a prismoid, add the areas of the 
two parallel sides and four times the area of a section taken 
midway between and parallel to them, and multiply this 
sum by | of the perpendicular distance between the paral- 
lel sides. 

This formula is used in the calculation of quantities of 
excavation and embankment on railroads, canals, etc. 



158 TABLE NO. 58^- 

From Trautwine's ** Civil En§pineer'8 Pocket Book.'* 



ANGLES. 



Approximate Measurement of Angles. 

(1) The four fingpers of the hand, held at right angles to the arm and 

at arm's length from the eye, cover about 7 degrees. And an angle of 7° corre- 
sponds to about 12.2 feet in 100 feet ; or to 36.6 feet in 100 yards ; or to 645 feet in a 
mile. 

(2) By means of a tw^o-foot rule, either on a drawing or between dis- 
tant objects in the field. If the inner edges of a common two-foot rule be opened 
to the extent shown in the column of inches, they will be inclined to each other 
at the angles shown in the column of angles. Since an opening of 3^ inch (up 
to 19 inches or about 10.5°) corresponds to from about }4° to 1°, no great accuracy 
is to be expected, and beyond 105° still less ; for the liability to error then in- 
creases very rapidly as the opening becomes greater. Thus, the last }/g inch cor- 
responds to about 12°. 

Angles for openings intermediate of those given may be calculated to the 
nearest minute or two, by simple proportion, up to 23 inches of opening, or 
about 147°. 

Table of Angles corresponding- to openings of a 2-foot rule. 

(Original). 

Correct. 



Ins. 


Deg. min.| 


Ins. ' 


}eg. rain.] 


Ins. 


Deg. min.l 


Ins. 


Deg.min.| 


Ins. 


Deg. min.j 


Ins. 


Deg. min. 


H 


1 


12 


4M ! 


20 


24 


814 


40 


13 


121.4 


61 


23 


I614 


85 


14 


20>i ' 


115 5 




1 


48 


1 


21 






40 


51 




62 


5 




86 


3 




116 12 


^ 


2 


24 


^ i 


21 


37 


yi 


41 


29 


yi 


62 


47 


>4 


86 


52 


Yi 


117 20 




3 


00 




22 


13 




42 


7 




63 


28 




87 


41 




118 30 


Vi 


3 


36 


% 


22 


50 


% 


42 


46 


% 


64 


11 


% 


88 


31 


% 


119 40 




4 


11 




23 


27 




43 


24 




64 


53 




89 


21 




120 52 


1 


4 


47 


5 


24 


3 


9 


44 


3 


13 


65 


35 


17 


90 


12 


'^^ 1 


122 6 




5 


23 




24 


39 




44 


42 




66 


18 




91 


3 


1 


123 20 


M 


5 


58 


% 


25 


16 


% 


45 


21 


M 


67 


1 


M 


91 


54 


M ' 


124 S6 




6 


34 




25 


53 




45 


59 




67 


44 




92 


46 




125 54 


3^ 


7 


10 


^ 


26 


30 


"A 


46 


38 


"A 


68 


28 


Vi 


93 


38 


Yi 


127 14 




7 


46 




27 


7 




47 


17 




69 


12 




94 


31 




128 35 


% 


8 


22 


% 


27 


44 


% 


47 


56 


H 


69 


55 


% 


95 


24 


% 


129 5» 




8 


58 




28 


21 




48 


35 




70 


38 




96 


17 




131 25 


2 


9 


34 


6 


28 


58 


10 


49 


15 


14 


71 


22 


18 


97 


11 


22 


132 53 




10 


10 




29 


35 




49 


54 




72 


6 




98 


5 




134 24 


M 


10 


46 


% 


30 


11 


"A 


50 


34 


Yi 


72 


51 


y^ 


99 


00 


Yi 


135 58 




11 


22 




30 


49 




51 


13 




73 


36 




99 


55 




137 35 


3^ 


11 


58 


)4 


31 


26 


H 


51 


53 


M 


74 


21 


% 


100 


51 


Yl 


139 16 




12 


34 




32 


3 




52 


33 




75 


6 




101 


48 




141 1 


% 


13 


10 


% 


32 


40 


?i 


53 


13 


% 


75 


51 


% 


102 


45 


% 


142 51 




13 


46 




33 


17 




53 


53 




76 


36 




103 


43 




144 46 


3 


14 


22 


7 


33 


54 


11 


54 


34 


15 


77 


22 


19 


104 


41 


23 


146 48 




14 


58 




34 


33 




55 


14 




78 


8 




105 


40 




148 58 


M 


15 


34 


V4, 


35 


10 


a 


55 


55 


M 


78 


54 


Ya 


106 


39 


M 


151 17 




16 


10 




35 


47 




56 


35 




79 


40 




107 


40 




153 48 


3^ 


16 


46 


^. 


36 


25 


14 


57 


16 


^ 


80 


27 


Y2 


108 


4] 


Yi 


156 34 




17 


22 




37 


3 




57 


57 




81 


14 




109 


43 




159 43 


%. 


17 


59 


% 


37 


41 


% 


58 


38 


% 


82 


2 


% 


110 


46 


Vi 


163 27 




18 


35 




38 


19 




59 


19 




82 


49 




HI 


49 




168 18 


4 


19 


12 


8 


38 


57 


12 


60 


00 


16 


83 


37 


20 


112 


53 


24 


180 00 




19 


48 




39 


35 




60 


41 




84 


26 




113 

1 


58 







(3) With the same table, using feet instead of inches. From 
any point measure 12 /ee< toward * each object, and place marks. Measure the 
distance in feet between these marks. Suppose the first column in the table to 
be ittt instead of inches. Then opposite the distance in jeet will be the angle. 



lin. =.083 ft. 

2 ins. = .167 ft. 

3 ins. = .25 ft. 



Yf, foot = 

4 ins. = .333 ft. 

5 ins. = .416 ft. 

6 ins. = .5 ft. 



1.5 inches. 

7 ins. = .583 ft. 

8 ins. = .667 ft. 

9 ins. = .75 ft. 



10 ins. = .833 ft. 

11 ins. = .917 ft. 

12 ins. = 1.0 ft. 



(4) Or, measure toward * each object 100 or any other number of 
flo^t, and place marks. Measure the distance in feet between the marks. Then 



Sine of half . 
the angle 



half the distance between the marks 



the distance measured toward one of the objects 
*rroni a table of sines^ Unci this angle and multiply it by J.'. 



159 
WEIGHT OF A CUBIC FOOT OF SUBSTANCES. 

Trautwine. 

Name of substances. Average weight, lbs. 

Alumintim, 162 

Brick, best pressed 150 

" common, hard 125 

soft ' 100 

Coal, Pennsylvania anthracite, solid 93 

" " '• broken, loose 54 

" '• " moderately shaken 58 

heaped bushel.... (77 to 83) 

" Bituminous, solid 84 

" " broken, loose 49 

" " heaped, loose bushel (74) 

Coke, loose 23 to 32 

'• heaped bushel 35 to 42 

Cement, Amei ican Hydraulic, Rosendale 56 

•' '• Louisville 50 

English " Portland 90 

Clay, loose 63 

Earth, common loam, dry, loose 76 

'' •' '• moderately rammed 95 

" as soft mud 108 

FHnt 162 

Glass ;... 157 

Gneiss 168 

Granite 170 

Gravel 90 to 106 

Ice 58.7 

Iron, cast 450 

" wrought 480 

Lead 711 

Lime, loose or in small lumps 53 

n " struck bushel .... [66] 

Limestone and marble 168 

'' loose, in fragments 96 

Masonry of Granite or limestone, well dressed 165 

" " mortar rubble 154 

" " sandstone, well dressed 144 

Mortar, hardened 103 

Quartz 165 

Salt, coarse 45 

" fine 49 

Sand, pure quartz, dry. loose 90 to 106 

' ' well Shaken : 99 to 117 

" wet 118 to 130 

Sandstone 151 

Shales 162 

Silver 655 

Snow, freshly fallen 5 to 12 

" moistened and compacted 15 to 50 

Steel 490 

Water, pure, 62.425 [Fuller], 62.37925 [HaswellJ approximately 62^3 

" sea 64.3 

WOODS 

Ash " 47 

Boxwood 60 

Cherry 42 

Cork 16 

Elm 35 

Hemlock 25 

Hickory 53 

Maple 35 

Oak, live 59, white 48, red or black .. . . 32 to 45 

Pine, white 25 yellow 35, southern — 45 

Green timber usually weighs from h to h more than dry. 



160 



TABLE NO. 59. 

:n^ails and spikes. 

Carnegie, Phipps & Co. 
Standard Steel Wire Nails. | Steel wire spikes. fCom'n. iron na'ls 





Long 


Common . 


Finishing. 


Long 


Diam 

ins. 


No. 
per lb 


Si. 


se. 
d 


Long 


No. 
per lb 


Size. 


Diam 
ins. 


No . 
per lb 


Diam 
ins. 


No. 
per lb 


2 d 


1 in. 


.0524 


1060 


.0453 


1558 


3 in. 


.1620 


41 


2 


1 in. 


800 


3 d 


U " 


.0588 


640 


.0508 


913 


.3A " 


.1819 


30 


8 


d 


U " 


400 


4 d 


U '^ 


.0720 


380 


.0508 


761 


4 " 


.2043 


23 


4 


d 


1* •• 


300 


5 d 


If " 


.0764 


275 


.0571 


500 


4i " 


.2294 


17 


5 


d 


If '• 


200 


6 d 


2 " 


.0808 


210 


.0641 


350 


5 " 


.2576 


13 


6 


d 


2 " 


1,50 


7 d 


U " 


.0858 


160 


.06411 315 1 


5A " 


.2893 


11 


7 


d 


2i " 


120 


8 d 


2i " 


.0935 


115 


.0720 214 \ 


6 " 


.2893 


10 


8 


d 


2J " 


85 


9 d 


21 " 


.0963 


93 


.0720 


195 


6i " 


.2249 


n 


9 


d 


2| " 


75 


10 d 


3 " 


.1082 


77 


.0808 


137 


7 " 


.2249 


7 


10 


d 


3 " 


60 


12 d 


3 J " 


.1144 


60 


.0808 


127 


8 " 


.3648 


5 


12 


d 


3^ " 


50 


16 d 


3^ '• 


.1285 


48 


.0907 


90 


9 " 


.3648 


U 


16 


d 


3| " 


40 


20 d 


4 " 


.1620 


31 


.1019 


62 








20 


d 


4 " 


20 


30 d 


4^" 


.1819 


22 












30 


d 


4i " 


16 


40 d 


5 " 


.2043 


17 












40 


d 


5 " 


14 


50 d 


5^ " 


.2294 


13 












50 


d 


H " 


11 


60 d 


6 •' 


.2576 


11 












60 


d 


6 " 


8 



TABLE NO. 60. 

WROUGHT SPIKES. 



Number to a keg of 150 pounds. 



Carnegie, Phipps <& Co. 



Length 

Ins. 


iin. 
No. 


TB in. 
No. 


fin. 
No. 


Length 
Ins. 


iin. 
No. 


A in. 
No. 


1 in. 

No. 


TB in. 
No. 


h in. 
No. 


3 


2250 
1890 
1650 
1464 
1380 
1292 






7 
8 
9 

10 
11 
12 


1161 


622 
635 
573 


482 
455 
424 
391 


445 

384 
300 
270 
249 
236 


306 


f 


1208 

1135 

1064 

930 

868 


■■742' 
570 


256 
240 

222 






203 


6 


:::::: :;.;.; 




180 



TABLE NO. fil. 
TABLE OP MANILLA ROPE. 



Trautwine. 



Diam- 


Circum- 
ference 
Inches . 


Wt. 

per ft 

lbs. 


Breaking load.] 


Diam- 
eter 
Inches. 


Cir- 

cumf. 

Ins. 


Wt. 

per ft 
lbs. 


Breaking load. 


eter 
Ins. 


Tons. 


Lbs. 


Tons. 


Lbs. 


.239 
.318 
.477 
.636 
.795 
.955 
1.11 


1 
1 

U 

2 

2i 

3 

3^ 


.019 
.033 
.074 
.132 
.206 
.297 
.404 


.25 
.35 
.70 
1.21 
1.91 
2.73 
3.81 


560 
784 

1 568 

2 733 
4 278 
6 115 
8 534 


1.27 
1.43 
1.59 
1.75 
1.91 
2.07 
2.23 


4 

5 

51 
6 
6^ 

7 


.528 
.668 
.825 
.998 
1.19 
1.39 
1.62 


5.16 
6.60 
8.20 
9.80 
11.4 
13.0 
14.6 


11 558 
14 784 
18 368 
21 952 
25 536 
29 120 
32 704 



161 



TABLE NO. 62. 



WELL DIGGING. 



r 1 cubic yard = 201.95 gallons. 




Idapted from 


Trautwine. 




Cubic yds . 




Cu. yds. 




Cubic yards 


Diameter 


for each 


Diameter 


for each 


Diameter 


for each 


in feet. 


foot of 


in feet. 


foot of 


in feet. 


foot in 




depth. 




depth . 




depth. 


1 


.0291 


3h 


.3.563 


6 


1.047 


i 


.0455 


f 


.4091 


i 


1.1:36 


i 


.0654 


4 


.4654 


i 


1.229 


i 


.0891 


i 


.5254 


i 


1.325 


2 


.1164 


i 


.5890 


7 


1.425 


i 


.1473 


f 


.6563 


i 


1.636 


i 


.1818 


5 


.7272 


8 


1.862 


1 


.2200 


i 


.8018 


1 

5 


2.102 


3 


.2618 


i 


.8799 


9 


2.356 


i 


.3073 


% 


.9617 


i 


2.625 



For diameters twice as great as those given in the table, 
for the cu. yds . of digging, take out those opposite ^ of the 
greater diam., and X by 4. Thus, for the cu. yds. in each foot 
of a well 12 ft. in diam., take out the yds. for a well of 6 ft. 
diam. andxby 4....1.074x4=4.188==cu. yds, for a well of 12 
feet diameter. 

TABLE NO. 63. 

CAPACITY OF CISTERNS IN GALLONS. 







For each 10 inches in 


deptk. 




Haswell. 


Diam. 


Gallons . 


Diam. 


Grallons . 


Diam. 


Gallons . 


Diam. 


Gallons. 


Feet. 




Feet. 




Feet. 




Feet. 




2. 


19.50 


5. 


122.40 


8- 


313.33 


12 


705.0 


2.5 


30.60 


5.5 


148.10 


8.5 


353.72 


13 


827.4 


3. 


44.60 


6. 


176.25 


9. 


396.56 


14 


959.6 


3.5 


59.97 


6.5 


206.85 


9.5 


461.40 


15 


1101.6 


4. 


78.33 


7. 


239.88 


10. 


489.60 


20 


1958.4 


4.5 


99.14 


7.5 


275.40 


11. 


592.40 


25 


3059.9 



In this table the capacity being given for 10 inches it is 
but necessary to divide by 10 by moving the decimal point 
one place to the left, in order to get the capacity for 1 inch . 
Thus, the capacity for 6 ft. diam and 10 inches deep =176.25 
gals., and for 1 inch deep it=17.625 gals. The capacity for 
any depths may be found by multiplying the capacity for 1 
inch by the depths in inches. Example. How many gals, 
in a cistern 12 feet in diam. and 9 feet deep ? 9 ft. =108 in. 
70.5, gals, in one inch, x 108=7614 gals. Ans. 

TABLE NO. 64. 

CAPACITY OF CISTERNS IN BARRELS. OF 31^ GALLONS. Leffel. 



Depth 


Diameter in feet. 


in feet. 


5 1 6 


7 


8 


9 
75.5 


10 


11 


12 


13 


14 


5 


23.3'33.6 


45.7 


59.7 


93.2 


112.8 


134.3 


157.6 


182.8 


6 


28.040.3 


54.8 


71.7 


90.6 


111.9 


135.4 


161.1 


189.1 


219.3 


7 


32.7i47.0 


64.0 


83.6 


105.7 


i:i0.6 


158.0 


188.0 


220.6 


255.9 


8 


37.353.7 


73.1 


95.5 


120.9 


149.2 


180.5 


214.8 


252.1 


292.4 


9 


42.0160.4 


82.2 


107.4 


136.0 


167.9 


203.1 


241.7 


283.7 


329.0 


10 


46.7 67.1 


91.4 


119.4 


151.1 


186.5 


225.7 


268.6 


315.2 


365.5 


11 


51.3i73 9 


100.5 


131.3 


166.2 


205.1 


24?. 2 


295.4 


346.7 


402.1 


12 


56.0;80.6 


109.7 


143.2 


181.3 


223.8 


270.8 


322.3 


378.2 


438.6 


13 


60.71-87.3 


118.8 


155.2 


196.4 


242.4 


293.4 


349.1 


409.7 


475.2 


14 


65.3194.0 


127.9 


167.1 


211.5 


261 . 1 


315.9 


376.0 


441.3 


511.8 



163 
ABAKREL. 

The standard wine barrel contains 313^ gals, of 231 cu. in. 
In Pennsylvania a wine bbl.=32 gals. The standard wine 
bbl. contains 4.211 cu. ft. A hogshead=63 gals. The aver- 
age size of the barrel used for oil or vinegar is about 193^ 
ins. diam. of head, 22^ ins. diam. of bung, and 29 to 30 ins. 
long and contains from 48 to 52 gals, the contents being 
usually marked on the head. 

In figuring on the barrel capacity of a cistern the size or 
volume of the barrel should be given or, in case of contract 
work, it should be specified. By reason of the size of the 
ordinary barrel being from 48 to 52 gals, it would, for con- 
venience, be best to figure on the basis of 50 gals, to the bbl. 
The bbl. of 313^ gals., however, is the one commonly used. 
MISCELLANEOUS. 

Shingles. 1000 laid 4 inches to the weather will cover one 

square of 100 sq. ft. and 5 Bbs of nails will lay them. 
Lath. 1000 will cover 70 sq. yds. of surface and 11 lbs. of 

nails will lay them. 
Mortar. 8 bushels of lime, 16 of sand and 1 of hair will 

make mortar fox 100 sq. yds, of surface. 
Stone Wall. 1 cord of stone, 3 bushels of lime, and 1 cu. 

yd. of sand will lay 100 cu. ft. of wall. 
Brick. 5 courses of brick will lay 1 foot high. 

6 brick in a course will lay a flue 4 by 12 inches. 

«' " " " 8 •' 16 '• 

" " •' •' " 12 " 12 " 

9 " " " ' " " 12 •' 16 '• 

10 " " " " " " 12 " 20 " 

TMckness of waU. No. to sq. ft. of wall. 

8 inches = 1 brick 14 

12 " li " 21 f No allowance being made for 

16 " 2 " 28 •< mortar or extra thickness of 

20 " 2i " 35 (brick. Brick 8 X 4 X 2 inches. 

24 " 3 " 42 

Flooring & Siding. Add ^ to the area to be covered to allow 
for lap. This is the lumberman's rule in selling. 

Hay. Get the number of cubic feet in the mow or stack; 
then, for new hay, divide by about 270 to get tons; for 
old hay, divide by about 230 to get tons; and for dry 
clover divide by about 310 to get tons. The weights of 
different grasses, in the different stages of dryness or 
compression, vary so greatly that any rule for weight by 
volume must be so purely arbitrary as to be of but 
little value. 

Corn. Get the cubic feet and. divide by 2}^ to get bushels. 

Apples, Potatoes, & Grain in Bin. Get cu. ft. and X by 8, 
then point off 1 place for decimals to get contents in 
bushels— or— from cubic ft. deduct i and the remainder 
=bushels in bin. (bush. =1.24445 cu. ft.) Example. — 
100 cu. ft. X 8=800, pointed off =80 bush.— or— 100— i (20) 
=80 bushels. 



163 



LUMBER TABLES. 
TABLE NO. 65. 



FEET, BOARE 


MEASURE, IN 


.JOIST, SCANTLING 


AND 


TIMBER. 


Length 
























in feet. 


lO 


12 


14 


16 


18 


20 


22 


24 


26 


28 


30 


Size in 
























Inches. 








FEET, BOARD MEASURE. 








2x4 


"^ 


— ^ 


9h 


101 


12 


134 


14S 


16 


"TtT 


18§ 


"lo 


2x6 


10 


12 


14 


16 


18 


20 


22 


24 


26 


28 


30 


2x8 


13^ 


16 


191 


2U 


24 


265 


294 


32 


341 


374 


40 


2x10 


161 


20 


m 


26| 


30 


334 


36| 


40 


434 


46| 


50 


2x12 


20 


24 


28 


32 


36 


40 


44 


48 


52 


56 


60 


2x14 


23i 


28 


321 


374 


42 


46| 


514 


56 


63§ 


654 


70 


3x4 


10 


12 


14 


16 


18 


20 


22 


24 


26 


28 


30 


3x6 


15 


18 


21 


24 


27 


30 


33 


36 


39 


42 


45 


3x 8 


20 


24 


28 


32 


36 


40 


44 


48 


52 


56 


60 


3xlO 


25 


30 


35 


40 


45 


50 


55 


60 


65 


70 


75 


3x12 


:« 


36 


42 


48 


54 


60 


66 


72 


78 


84 


90 


3x|4 


35 


42 


49 


56 


63 


70 


77 


84 


91 


98 


105 


4x 4 


m 


16 


181 


21i 


24 


26| 


294 


32 


34§ 


374 


40 


4x 6 


20 


24 


28 


32 


36 


40 


44 


48 


52 


56 


60 


4x 8 


261 


32 


37^ 


421 


48 


534 


581 


64 


694 


74| 


80 


4x10 


33^ 


40 


46| 


534 


60 


661 


734 


80 


86S 


934 


100 


4x|2 


40 


48 


56 


64 


72 


80 


88 


96 


104 


112 


120 


6x 6 


30 


36 


42 


48 


54 


60 


66 


72 


78 


84 


90 


6x 8 


40 


48 


56 


64 


72 


80 


88 


96 


104 


112 


120 


6xlO 


50 


60 


70 


80 


90 


100 


110 


120 


130 


140 


150 


6x12 


60 


72 


84 


96 


108 


120 


132 


144 


156 


168 


180 


8x 8 


m 


64 


74i 


854 


96 


106S 


1174 


128 


1381 


1494 


160 


8xlO 


66i 


80 


93i 


1061 


120 


1334 


146-1 


160 


1734 


1861 


200 


8x12 


80 


96 


112 


128 


144 


160 


176 


192 


208 


224 


240 


lOxlO 


83i- 


100 


117 


13:3 


150 


167 


183 


aoo 


217 


233 


250 


10xl2 


100 


120 


140 


160 


180 


200 


220 


240 


260 


280 


300 


J 2x1 2 


120 


144 


168 


192 


216 


240 


264 


288 


312 


336 


360 


12x14 


140 


168 


196 


224 


252 


280 


:308 


336 


364 


392 


420 


I4x(4 


163J 


196 


2281 


2614 


294 


3261 


3594 


392 


424§ 


4574 


490 



TABLE NO. 66. 

FEET— BOARD MEASURE, IN 1 INCH BOARDS. 



New 



Width 


Length in feet. 


m 


8 




12 




16 




20 




24 


inches. 




10 




14 




18 




22 




4 


2% 


3K 


4 


m 


5^ 


6 


6% 


7i/f( 


8 


6 


4 


5 


6 


7 


8 


9 


10 


11 


12 


8 


5K 


^% 


8 


9K 


10% 


12 


13^ 


14% 


16 


10 


6^/. 


8K 


10 


n% 


13M 


15 


1«% 


181^ 


20 


12 


8 


10 


12 


14 


16 


18 


20 


22 


24 


14 


9K 


n% 


14 


16><( 


18% 


21 


23^ 


25% 


28 


16 


10^ 


v^% 


16 


l^% 


21K 


24 


26% 


29K 


32 


18 


12 


15 


18 


21 


24 


27 


30 


33 


36 


20 


13K 


i^% 


20 


23K 


26% 


30 


33M 


36% 


40 



RULE for estimating ft. b. m. in any piece of board or timber.— [A foot 
b. m. = 12 X 12 inches bj' 1 inch thick, = 144 cubic inches.] Multiply the 
width by the thickness -^ product by 12 and X quotient by length. Thus : 

A stick 8 by 10 inches by 10 feet equals 8 X 10 = 80 inches of sectional 

area which -^ 12 =6% ft. b. m. per foot of length ; this X 10 = 66% ft. 

3" by 12 ■ by 10 equals 3 X 12= 36. 36-^12 = 3, 3 X 10 = 30 ft. B.M. 

4" by 6" by 10' equals 4 X 6 = 24, 24 -4- 12 = 2, 2 X 10 = 20 ft. B.M.&c. 



From Trantwine's *' Civil £ii^ineer*s Pocket Book. 



l<eii$:fths of a Dejarr^c or liOng'itnde in different fjatitmles, 

and at the level of the Sea. These lengths are in common land or statute miles, 
of a^bO ft. Since the figure of the earth has never been precisely ascertained, these are but close ap 
proximations. Intermediate ones maybe found correctiv by simple proportion. 1° of longitude 
corresponds to 4 mins of civil or cl(ick time ; 1 min of longitude to i sees of time. 



Degof 
Lat. 


Miles. 


Degof 
Lat. 


Miles. 


Degof 
Lat. 


Miles. 


Degof 
Lat. 


Miles. 


Degof 
Lat. 


Miles. 


Degof 
Lat. 


Miles. 





69.16 


14 


67.12 


28 


61.11 


42 


51.47 


56 


38.76 


70 


23.72 


2 


69.12 


16 


66.50 


30 


59.94 


44 


49.83 


58 


36.74 


72 


21.43 


4, 


68.99 


18 


65.80 


32 


58.70 


46 


48.12 


60 


34.67 


74 


19.12 


6 


68.78 


20 


65.02 


34 


57.39 


48 


46.36 


62 


32.55 


76 


16.78 


8 


68.49 


22 


64.15 


36 ! 


56.01 


50 


44.54 


64 


30.40 


78 


14.42 


10 


68.12 


24 


63.21 


38 1 


54.56 


52 


42.67 


66 


28.21 


80 


12.05 


12 


67.66 


26 


62.20 


40 1 


53.05 


54 


40.74 


68 


25.98 


82 


9.66 







Inches reduced to Decimals < 


>f a 


Foot. 


No error,s. 


Ins. 


Foot. 


Ins. 


Foot. 
.1667 


Ins. 


Foot. 


Ins. 


Foot. 


Ins. 


Foot. 


Ins. 


Foot. 





.0000 


2 


4 


.3 ;.;■! 


6 


.5000 


8 


.6667 


lO 


.8333 


1-32 


.0026 




.1693 




.3.J59 




.5026 




.6693 




.8359 


1-16 


.0052 




.1719 




.33^5 




.5052 




.6719 




.8385 


3-32 


.0078 




.1745 




.3411 




.5078 




.6745 




.8411 


H 


.0104 


H 


.1771 


'A 


.3438 


M 


.5104 


Ji 


^.6771 


% 


.8438 


5-32 


.0130 




.1797 




.3461 




.5130 




.6797 




.8464 


3-16 


.01.56 




.1823 




.3190 




.5156 




.6823 




.8490 


7-32 


.0182 




.1819 




.3316 




.5182 




.6849 




.8516 


M 


.0208 


H 


.1875 


% 


.,3542 


M 


.5208 


Va 


.6875 


M 


.8542 


9-32 


.0234 




.1901 




.3568 




.5234 




.6901 




.8568 


516 


.0260 




.1927 




..3594 




.5260 




.6927 




.8594 


11-32 


.0286 




.1953 




.3620 




.5286 




.6953 




.8620 


H 


.0313 


% 


.1979 


% 


.3646 


% 


.5313 


% 


.6979 


% 


.8646 


13-32 


.0339 




.2005 




.3672 




.5339 




.7005 




.8672 


7-16 


.0365 




.2031 




..3698 




.5365 




.7031 




.8698 


15-32 


.0391 




.2057 




.8724 




.5391 




.7057 




.8724 


14 


.0417 


% 


.20t.j 


^■i 


.3750 


li 


.5417 


Vi 


.7083 


\*i 


.8750 


17-32 


.0443 , 




.2109 




.3776 




.5443 




.7109 




.6776 


9-16 


.016:) 




.2135 




.3802 




.5469 




.7135 




.8802 


19-32 


.0W5 




.2161 




.3828 




.5495 




.7161 




.8828 


% 


.0521 


Y% 


.2188 


% 


.3854 


% 


.5521 


% 


.7188 


% 


.8854 


21-32 


.0547 




.2214 




.3880 




.5547 




.7214 




.8880 


11-16 


.0573 




.2240 




.3906 




.5573 




.7240 




.8906 


23-32 


.059 J 




.2263 




.3932 




.5599 




.7266 




.893-2 


H 


.0625 


Vi 


.22:12 


H 


.3958 


H 


.5625 


% 


.7292 


% 


.8958 


25-32 


.0651 




.2318 




.3984 




.5651 




.7318 




.8984 


13-16 


.0377 




.2344 




.4010 




.5677 




.7344 




.9010 


2--.S2 


.0703 




.2370 




.4036 




.5703 




.7370 




.9036 


% 


.0729 


% 


.2396 


Yi 


.4063 


% 


.5729 


y» 


.7396 


% 


.9063 


29 32 


.0755 




.2422 




.4089 




.5755 




.7422 




.9089 


15 16 


.0781 




.2448 




.4115 




.5781 




.7448 




.9115 


31-32 


.0807 




.2474 




.4141 




.5807 




.7474 




.9141 


1 


.0833 


3 


.2500 


5 


.4107 


7 


.5833 ■ 


9 


.7500 


11 


.9167 


1-32 


.0859 




.2526 




.4193 




.5859 




.7526 




.9193 


1-16 


.0885 




.2552 




.4219 




.5885 




.7552 




.92)9 


3-32 


.0911 




.2578 




.4215 




.5911 




.7578 




.9245 


H 


.0938 


M 


.2601 


M 


.4271 


H 


.5938 


}i 


.7604 


M 


.9271 


5-32 


.0964 




.2630 




.4297 




.5<)f.4 




.7630 




.9297 


3-16 


.0990 




.2356 




.4323 




.5s:yo 




.7656 




.9323 


7-32 


.1016 




.2682 




.4349 




.6016 




.7682 




.9349 


M 


.1042 


M 


.2708 


}4 


.4375 


}4 


.6042 


K 


.7708 


Va. 


.9375 


9-32 


.1068 




.2734 




.4401 




.6068 




.7734 




.9401 


616 


.1094 




.2760 




.4427 




.6094 




.7760 




.9427 


11-32 


.1120 




.2786 




.4453 




.6120 




.7786 




.9453 


% 


.1146 


% 


.2813 


% 


.4479 


% 


.6146 


% 


.7813 


% 


.9479 


l.'l-32 


.1172 




.28.39 




.4505 




.6172 




.7839 




.9505 


'-16 


.1198 




.2865 


> 


.4531 




.6198 




.7865 




.9531 


15-32 


.1224 




.2891 




.4557 




.6224 




.7891 




.9557 


14 


.1250 


Vi 


.2917 


ii 


.4.583 


M 


.6250 


^ 


.7917 


M 


.9583 


17-32 


.1276 




.2943 




.4609 




.6276 




.7943 




.9609 


9-16 


.1302 




.2969 




.4635 




.6302 




.7969 




.9635 


19-32 


.1328 




.2995 




.4661 




.6328 




.7995 




.9661 


% 


.1354 


% 


.3021 


% 


.4688 


% 


.6354 


% 


.8021 


5S 


.9688 


21-32 


.1380 




.3047 




.4714 




.6380 




.8047 




.9714 


11-16 


.1406 




.8073 




.4740 




.6406 




.8073 




.9740 


23-.H2 


.1432 




.3099 




.4766 




.6432 




.8099 




.9766 


H 


.1458 


% 


.3125 


% 


.4792 


% 


.6458 


y* 


.8125 


% 


.9792 


25-32 


.1484 




.3151 




.4818 




.6484 




.8151 




.9818 


13-16 


.1510 




.3177 




.4844 




.6510 




.8177 




.9844 


27-32 


.1536 




.3203 




.4870 




.6536 




.8203 




.9870 


K 


.156;^ 


y» 


.3229 


y» 


.4896 


% 


.6563 


% 


.8229 


% 


.98S«> 


»32 


.1,589 




.3255 




,4922 




.6589 




.8255 




.9922 


15--.6 


.1615 




.3281 




.4948 




.6615 




.8281 




.9948 


81-82 


.1641 




.3307 




.4974 




.6641 




.8307 




.9974 



165 



TABLE NO. 68. 

DECIMALS OF AN INCH FOR EACH ^^th. INCH. 



^ds. 


B^^ths. 


Decimal. 


Fraction. 


s^ds. 


B^ths. 


Decimal. 


Fraction. 




1 


.015625 






33 


.515625 




1 


2 


03125 




17 


34 


.53125 




2 


3 
4 


1046875 
.0625 


1-16 


18 


35 
36 


.546875 
.5625 


9-16 




5 


.078125 






37 


.578125 




3^ 


6 


.09375 




19 


38 


.59375 






7 


109375 






39 


.609375 




4 


8 


;i25 


1-8 


20 


40 


.625 


5-8 




9 


. 140625 






41 


.640625 




5 


10 


. 15625 




21 


42 


.6.5625 






11 


171875 






43 


.671875 




6 


12 


.1875 


3-16 


22 


44 


.6875 


11-16 




•13 


. 203125 






45 


.703125 




7 


14 


21875 




23 


46 


.71875 






15 


.234375 






47 


.734375 




8 


16 


.25 


1-4 


24 


48 


.75 


3-4 




17 


.265625 






49 


.765625 




9 


18 


.28125 




25 


50 


.78125 






19 


.296875 






51 


.796875 




10 


20 


.3125 


5-16 


26 


52 


.8125 


13-16 




21 


.328125 






53 


.828125 




11 


22 


. 34375 




27 


54 


.84375 






23 


.359375 






55 


.859375 




12 


24 


.375 


3-8 


28 


56 


.875 


7-8 




25 


.390625 






57 


.890625 




13 


26 


.40625 




29 


58 


.90625 






27 


.421875 






59 


.921875 




14 


28 


.4375 


7-16 


30 


60 


.9375 


15-16 




29 


.453125 






61 


.953125 




15 


:% 


.46875 




31 


62 


.96875 






31 


.484375 






63 


.984375 




16 


32 


.5 


1-2 


32 


64 


1 


J 



166 



TABLE NO. 69. 



From Traiitwine's *' Civil Engineer's Pocltet Book.'" 

HYDRAULICS. 



TABIiE Of the square roots of the fifth powers of num- 

bers. In this table the iium Iters and the roots are supposed to be in the- same di- 
mensions ; that is, both in inches, or both iu feet. &c. See the next table. 



No. 



.25 

.5 

.75 

1. 

1.25 

1.5 

1.75 

2. 

2.25 

2.5 

2.75 

3. 

3.25 

3.5 

3.75 

4. 

4.25 

4.5 

4.75 

5. 

5.25 

5.5 

5.75 

6. 

6.25 

6.5 

6.75 



Sq. Rt. 
of 5th 
Power. 



.031 
.177 
.485 
1. 

1.747 
2.756 
4.051 
5.657 
7.594 
9.882 
12.541 
15.588 
19.042 
22.918 
27. 232 
32. 
37.24 
42.96 
49.17 
55.90 
63.15 
70.94 
79.28 
88.18 
97.66 
107.72 
118.38 



No. 



7. 

7.25 

7.5 

7.75 

8. 

8.25 

8.5 

8.75 

9. 

9.25 

9.5 

9.75 

10. 

10.5 

II. 

11.5 

12. 

12.5 

13. 

13.5 

14. 

14.5 

15. 

15.5 

16. 

16.5 

17. 



Sq. Rt. 




Sq. Rt. 


of 5th 


No. 


of 5tli 


Power. 




Power. 


129.64 


17.5 


1281.1 


141.53 


18. 


]:J74 6 


154.05 


18.5 


1472.1 


167.21 


19. 


1573.6 


181.02 


19.5 


1679,1 


195.50 


20. 


1788.9 


210.64 


20.5 


1902.8 


226.48 


21. 


2020.9 


24.S. 


21.5 


2143.4 


260.23 


22. 


2270.2 . 


. 278.17 


22.5 


2401.4 


296.83 


23. 


2537. 


318.23 


23.5 


2677.1 


357.2 


24. 


2821.8 


401.3 


24.5 


2971.1 


448.5 


25. 


3125. 


498.8 


25.5 


3283.6 


552.4 


26. 


3446.9 


609.3 


26.5 


3615.1 


669.6 


27. 


3788. 


733.4 


27.5 


3965.8 


800.6 


28. 


4148.5 


871.4 


28.5 


4336.2 


945.9 


29. 


4528.9 


1024. 


29.5 


4726.7 


1105.9 


30. 


4929.5 


1191.6 


30.5 


5138. 



31. 

31.5 

32. 

32.5 

33. 

33.5 

34. 

34.5 

35. 

35.5 

36. 

36.5 

37. 

37.5 

38. 

38.5 

39. 

39.5 

40. 

41. 

42. 

43. 

44. 

45. 

46. 

47. 

48. 



Sq. Rt. 
of 5th 
Power. 



5351 

6569 

5793 

6022 

6256 

6496 

6741 

6991 

7247 

7509 

7776 

8049 

8327 

8611 

8901 

9197 

9498 

9806 

10119 

10764 

11432 

12125 

12842 

13584 

14351 

15144 

35Sb3 





Sq. Rt. 




Sq. Rt. 


No. 


of 5 th 


No, 


of 5th 




Power. 




Power. 


49 


16807 


76 


50354- 


50 


17678 


77 


52027 


51 


18575 


78 


53732 


52 


19499 


79 


55471 


53 


20450 


80 


57243 


54 


21428 


81 


59049 


55 


22434 


82 


60888 


56 


23468 


83 


62762 


57 


24529 


84 


64669 


58 


25620 


85 


66611 


59 


26738 


86 


68588 


60 


27886 


87 


70599 


61 


29062 


88 


72646 


62 


30268 


89 


74727 


63 


31503 


90 


76843 


64 


32768 


91 


78996 


65 


34063 


92 


81184 


66 


35388 


93 


83408 


67 


36744 


94 


85668 


68 


38131 


95 


87965 


69 


395^ 


96 


90298 


70 


40996 


97 


92668 


71 


42476 


98 


95075 


72 


43988 


99 


97519 


73 


45531 


100 


100000 


74 


47106 






75 


48714 







Numbers, in inches. Square roots of fifth powers, in feet. 





Sq. Rt. of 




Sq. Rt. of 




Sq. Rt. of 




Sq. Rt. of 




Sq. Rt. of 




5th Pow. 




5th Pow. 




5th Pow. 




5th Pow. 




5th Pow. 


Ins. 


Feet. 


Ins. 


Feet. 


Ins. 


Feet. 


Ins. 


Feet. 


Ins. 


Feet. 


M 


.00006 


39i 


.0547 


12. 


1.000 


22M 


4.813 


42 


22.92 


y» 


.00017 


4. 


.0641 


}4 


1.108 


23 


5.086 


43 


24.31 


H 


.00035 


Va 


.0731 


13. 


1.221 


H 


5.365 


44 


25.74 


% 


.00062 


% 


.0827 


% 


1.342 


24 


5.657 


45 


27.23 


% 


.00098 


K 


.0971 


14. 


1.470 


25 


6.264 


46 


28.77 


% 


.00144 


5. 


.1120 


M 


1.605 


26 


6.909 


47 


30.36 


1. 


.0020 


>i 


.1271 


15. 


1.747 


27 


7.593 


48 


32.00 


H 


.0027 


H 


.1428 


H 


1.896 


28 


8.316 


49 


33.69 


H 


.0035 


H 


.1590 


16. 


2.053 


29 


9.079 


50 


35.44 


% 


.0044 


6. 


.1768 


^ 


2.217 


30 


9.882 


51 


37.25 


^ 


.0055 


J4 


.2160 


17. 


2.389 


31 


10.73 


52 


39.13 


% 


.0067 


7. 


.2599 


}4 


2.567 


32 


11.61 


53 


41.02 


H 


.0081 


% 


.3088 


18. 


2.756 


.S3 


12.54 


54 


42.96 


■a 


.0096 


8. 


.3628 


% 


2.950 


34 


13.51 


55 


44.97 


3. 


.0113 


H 


.4228 


19. 


3.155 


35 


14.53 


56 


47.05 


a 


.0152 


9. 


.4871 


M 


3.365 


36 


15.59 


57 


49.17 


}i 


.0198 


H 


.5577 


20. 


3.586 


37 


16.69 


58 


51.35 


H 


.0252 


10. 


.6339 


Ji 


3.813 


38 


17.84 


59 


53.60 


s. 


.0312 


H 


.7162 


21. 


4.051 


39 


19.04 


60 


55.90 


K 


.0383 


U. 


.8043 


^ 


4.297 


40 


20.29 


61 


58.27 


H 


m^ 


« 


.8990 


22. 


4.551 


41 


21.58 







mf^n&m 



From Trautwiiio'K "Civil Eiiaiiieer's Pocket Book." 



MENSURATION. 



To find the leng^th of a circular arc by the following table. 



Knowing the rad of the circle, and the measure of the arc in deg, min, &c. 

Rule. Add together the leirgths in the table found respectively opposite to the deg, min, &o, of 
the arc. Mult the sum by the rad of the circle. 
Ex. In a circle of 12.43 feet lad, is an arc of 13 deg, 27 min, 8 sec. How long is the arc? 
Here, opposite 13 deg in the table, we find, .2268928 
27 rain " " " .0078540 

8 sec " " " .0000388 

Sum = .2347856 
And .^347856 X 12.43 or rad = 2.918385 feet, the reqd length of arc. 



I.EJVGTHS OF CIRCri^AR ARCS TO RAD 1. 



No errors. 



Deg. 


Length. 


Deg. 


Length. 


Deg. 


Length. 


Min. 


Length. 


Sec. 


Length. 


1 


.0174533 


61 


1.0646508 


121 


2.1118484 


1 


.0002909 


1 


.0000048 


2 


.034906H 


62 


1.0821041 


122 


2.1293017 


2 


.0005818 


2 


.0000097 


3 


.0523593 


63 


1.0995574 


123 


2.1467550 


3 


.0008727 


3 


.0000145 


4 


.0698132 


64 


1.1170107 


124 


2.1642083 


4 


.0011636 


4 


.0000194 


5 


.0872665 


65 


1.1344640 


125 


2.1816618 


5 


.0014544 


5 


.0000242 


6 


.1047198 


66 


1.1519173 


126 


2.1991149 


6 


.0017453 


6 


.0000291 


7 


.1221730 


67 


1.1639706 


127 


2.2165682 


7 


.0020382 


T 


.0000339 


8 


.1396263 


68 


1.1868239 


128 


2.2340214 


8 


.0023271 


8 


.0000388 


9 


.1570796 


69 


1.2042772 


129 


2.2514747 


9 


.0026180 


9 


.0000436 


10 


.1745329 


70 


1.2217305 


1.30 


2.2689280 


10 


.0029089 


10 


.0000485 


11 


.1919862 


71 


1.2391838 


131 


2.2863813 


11 


.0031998 


11 


.0000533 


12 


.2094395 


72 


1.2566371 


132 


2.3038346 


12 


.0034907 


12 


.0000582 


13 


.2268928 


73 


1.2740904 


133 


2.3212879 


13 


.0037815 


13 


.0000630 


14 


.2443461 


74 


1.2915436 


134 


2.3387412 


14 


.0040724 


14 


.0000679 


15 


.2617994 


75 


1.3089969 


135 


2.3561945 


15 


.0043633 


15 


.0000727 


16 


.2792527 


76 


1.3264502 


136 


2.3736478 


16 


.0046542 


16 


.0000776 


17 


.2967060 


77 


1.3439035 


137 


2.S911011 


17 


.0049451 


17 


.0000824 


18 


.3141593 


78 


1.3613568 


138 


2.4085544 


18 


.0052360 


18 


.0000873 


19 


.3316126 


79 


1.3788101 


139 


2.4260077 


19 


.0055269 


19 


.0000921 


20 


.3490659 


83 


1..3932334 


140 


2.4434610 


20 


.0058178 


20 


.0000970 


21 


.3665191 


81 


1.4137167 


141 


2. -1609142 


21 


.0061087 


21 


.0001018 


22 


.3839724 


82 


1.43117 K) 


142 


2.4783675 


22 


.0063995 


22 


.0001067 


23 


.4014257 


83 


1.44832^3 


143 


2.4958208 


23 


.0066904 


23 


.0001115 


24 


.4188790 


84 


1.4660768 


144 


2.5132741 


24 


.0069813 


24 


.0001164 


25 


. 43633 J3 


85 


1.4835299 


145 


2.5307274 


25 


.0072722 


25 


.0001212 


26 


.4537856 


86 


1.50098.02 


146 


2.5481807 


28 


.0075631 


26 


.0001261 


27 


.4712389 


87 


1.5184)64 


147 


2.5656340 


27 


.0078540 


27 


.0001309 


28 


.4886922 


88 


1.5358397 


148 


2.5830873 


28 


.0081449 


28 


.0001357 


29 


.5061455 


89 


1.553343) 


149 


2.6005406 


29 


.0084358 


29 


.0001406 


30 


.5235988 


90 


1.57079,i3 


150 


2.6179t39 


30 


.0087266 


30 


.0001454 


31 


.5410521 


91 


1.588219:; 


151 


2.6354472 


31 


.0090175 


31 


.0001503 


32 


.5585054 


92 


1.63o7.')29 


152 


2.6529005 


32 


.00930S4 


32 


.0001551 


33 


.5759587 


93 


1.6231562 


153 


2.6703538 


33 


.0095963 


33 


.0001600 


84 


.5934119 


94 


1.6 106095 


154 


2.6878070 


34 


.0098902 


34 


.0001648 


35 


.6108652 


95 


1.6580628 


135 


2.7052603 


35 


.0101811 


35 


.0001697 


36 


.6283185 


96 


1.6755161 


156 


2.7227136 


36 


.0104720 


36 


.0001745 


37 


.6457718 


97 


1.69J969t 


157 


2.7401669 


37 


.0107629 


37 


.0001794 


38 


.6632251 


98 


1.7104227 


158 


2.7576202 


38 


.0110538 


38 


.0001842 


39 


.680678:- 


99 


1.7278760 


159 


2.7750735 


39 


.0113446 


39 


.0001891 


40 


.6981317 


100 


1.7453293 


160 


2.7925268 


40 


.01163C3 


40 


.0001939 


41 


.7155850 


101 


1.7627825 


161 


2.8099801 


41 


.01U264 


41 


.0001988 


42 


.7330383 


102 


1.7802358 


162 


2.82743:^4 


42 


.0122173 


42 


.0002036 


43 


.7504916 


103 


1.7976:-91 


163 


2.8448867 


43 


.0125082 


43 


.0002085 


44 


.7679149 


104 


1.8151424 


164 


2.88-J3t00 


44 


.0127991 


44 


.0002133 


45 


.785WS2 


105 


1.8325957 


185 


2 8797933 


45 


.0130900 


45 


.0002182 


48 


.8023515 


ne 


1.8500 t90 


168 


2.*972468 


46 


.0133809 


46 


.0002230 


47 


.S20:?0n 


107 


1.807)020 


167 


2.9146999 


47 


.01.36717 


47 


.0002279 


48 


.8377530 


1-08 


1.88t95.5fi 


168 


2.:in2i53i 


48 


.0139626 


48 


.0002327 


49 


.8552113 


109 


1.9024089 


189 


2.9496084 


49 


.0142535 


49 


.0002376 


50 


.8726S13 


110 


1.9:98822 


170 


2.9870,597 


50 


.0145444 


50 


.0002424 


51 


.8951179 


111 


1.9.373r5 


171 


2.9'5451.30 


51 


.0148353 


51 


.0002473 


52 


.90757:2 


112 


1.9547688 


172 


3.0019683 


52 


.0151262 


52 


.0002521 


53 


.92502(5 


113 


1.9722221 


170 


3.0194196 


53 


.0154171 


53 


.0002570 


54 


.91?t77S 


1-4 


i!98w:.-'3 


1T4 


^M68729 


54 


.0157080 


54 


.0002618 


53 


.95331: 1 


115 


2.007: '^Sf, 


175 


55 


.0159989 


55 


.0002666 


56 


.9770ni 


116 


1 2.n24.-.'*'9 


!T(i 


i:nffiym 


.56 


.0182897 


56 


.0002715 


57 


.994=5377 


117 


2.0t20!n2 


177 


^.(M*if::^'>fi 


57 


018.5806 


57 


.0002763 


58 


1.0122910 


118 


2.n5948s.i 


ITS 


'iAti-^FMn 


58 


.0168715 


58 


.0002812 


59 


1.0297+43 


119 


2.0789418 


179 


3.!\'41:h94 


59 


.0171624 


59 


.0002860 


60 


1.0471976 


120 


i 2.0943951 


180 


3 1415927 


60 


.0174533 


60 


.0002909 



168 

EXPLAINATION OF TABLES OF CIRCLES. 
It will be noticed that there are three tables of circles. 

Fl RST —Table giving diameters in units and e I GHTHS. 
SECOND- '• " " " " " TENTHS 

THIRD — " " '• " " •' TWELFTHS. 

The diameter in all cases extending to 100. 
The following rules with reference to the table giving the 
diameters in TENTHS will also be of value. 

To compute the area or circumference of a diameter great- 
er than 100 and less than 1001; 

Rule — Take out the area or circumference from the table 
as though the number had one decimal, and move the deci- 
mal point two places to the right for area and one place 
for the circumference. 

Example — Wanted the area and circumference of 567. The 
tabular area for 56.7 is 2524.9687, and circumference 178.1283. 
Therefore area for 567=252496.87 and circumf. =1781.283. 

To coraptue the area or circumference of a diameter 
greater than 1000. 

Rule— Divide by a factor 2, 3, 4, 5, etc., if practicable, that 
will leave a quotient to be found in the table; then multi- 
ply the tabular area of the quotient by the square of the 
factor, to get required area; and the tabular circumference 
by the factor to get the required circumference. 

Example— Wanted the area and circumference of 2109. 
Dividing by 3 the quotient is 703, for which the area is 
388,150.84 and the circumference 2208.54. Therefore area 
of 2109 = 388150.84 X 9 ( 9 = square of 3 ) = 3493357.56, and 
the circumference = 22 08.54 X 3 = 6625.63. 

The following rules with reference to table giving the 
diameters in EIGHTHS will also be found of value. 

If the required diameter is not in the table, separate it 
and take the circumference of each and add them. 

Example— Wanted the circumference of 25|^ inches. 
Circumference of 25 in.=78.5398 and of ^=2.06167; adding 
these we get 80.60147 the required circumference. This pro- 
cess will not answer for the area, however. In case the 
area is wanted, reduce the given diameter to a decimal and 
multiply this by itself and the product by .7854 (area = square 
of diameter X. 7854). Reduce to a decimal of a foot or of an 
inch by use of tables 67 and 68. See AREA P. 152. 

Where the diameter contains more than one decimal, or 
where it contains fractions of an inch, see small tables 
following the tables giving diameters in TENTHS & 
TWELFTHS respectively, on pages 177 and 184. 

See rules on page 152 for calculating diameters, circum- 
ferences, or areas, or the sides of equal squares, without the 
use of tables. 



TABLE NO. 71. 169 

From Trautwine's "livi* Kngineer's Pocket Book.'' 



CIRCLES. 



TABLE 1 OF CIRCLES. 

Diameters tn units and eightlis, dtc. 

Circumferences or areas intermediate of those in this table, may be found by sim- 
ple arithmetical proportion. No errors. 



Diam. 


Clrcumf. 


Area. 


Diam. 


Clrcumf. 


■ Area. 


Diam. 


Circumf. Area. 


Oiam. 


Circumf. 


Area, 


1-64 


.049087 


.00019 


3. H 


10.9956 


9.6211 


10)^ 


31.8086 80.516 


19 V4 


60.4757 


291.04 


1-32 


.098175 


.00077 


9-16 


11.1919 


9.9678 


M 


32.2013 


82.516 


% 


60.8684 


294.83 


3-64 


.147262 


.00173 


H 


11.3883 


10..321 


% 


32.594a 


84.541 


Vi 


61.2611 


298.65 


1-16 


.196.350 


.00.507 


11-16 


11.5846 


10.680 


H 


32.9867 


86.590 


% 


61.6538 


302.49 


3-32 


.291524 


.00690 


•?4 


11.7810 


11.045 


H 


33.3794 


88.664 


Vi 


62.0465 


306.35 


M 


.392699 


.01227 


13-16 


11.9773 


11.416 


% 


33.7721 


90.763 


Va 


62.4392 


310.24 


5-32 


.490874 


.01917 


% 


12.17:i7 


11.793 


% 


34.1648 


92.886 


20. 


62.8319 


314.16 


3-16 


589019 


.0';761 


15-16 


12. .3700 


12.177 


11. 


34.5575 


95.033 


% 


63.2246 


318.10 


7-32 


.687223 


.03758 


4. 


i2.5);it 


12.566 


y» 


34.9502 


97.205 


Vi 


63.6173 


322.06 


M 


.78.5398 


.01)0) 


1-16 


12.7627 


12.9.')J 


/4 


35.3429 


99.402 


% 


64.0100 


326.05 


932 


.88 !573 


.Oliil.i 


"4 


12 95 J 1 


1-.'.361 


i*8 


35.7356 


101.62 


'i 


64.4026 


330.06 


516 


.981748 


.071)70 


3-lt) 


13.1554 


13.772 


.4 


36.1283 


103.87 


% 


64.7953 


334.10 


11-32 


1.07992 


Ml'Sl 


/4 


13.3518 


14.186 


% 


36.5210 


106.14 


y* 


65.1880 


338.16 


% 


1.17810 


.11015 


5-16 


13.5481 


14.607 


H 


36.9137 


108.43 


y% 


65.5807 


342.25 


13-32 


1.27627 


.12.).52 


?8 


13.7 445 


15.0 5.) 


% 


37.;5064 


110.75 


21. 


65.9734 


346.36 


7-16 


1.37445 


.150.5) 


7-16 


13 91'):! 


15.4615 


12. 


37.6991 


113.10 


% 


66.3661 


350.50 


15-32 


1.47262 


.17257 


H 


14.1572 


15.904 


Vi 


.38.0918 


115.47 


M 


66.7588 


354.66 


hi 


1.57080 


.19635 


9-16 


14.3.i.J5 


16.349 


Vi 


38.4845 


117.86 


% 


67.1515 


358.84 


17-32 


1.66897 


.2216) 


^i 


14.52) J 


16.800 


% 


38.8772 


120.28 


% 


67.5442 


363.05 


916 


1.76715 


.218)) 


11-16 


14.7232 


17 257 


u, 


39 2699 


122.72 


% 


67.9369 


367.28 


19-32 


1.86)32 .27.!SS 


H 


I4.9ri;i 


17.721 


% 


39.6626 


125.19 


% 


68.3296 


371.54 


^ 


I 9o3o0 .303-S) 


13-li 


15.118) 


18.190 


% 


40.0553 


127.68 


% 


68.7223 


375.83 


21-32 


2.06167 


.3.!Sil 


Vs 


15.5155 


18.665 


% 


40.4480 


130.19 




69.1150 


380.13 


11-16 


2.15984 


.37122 


15-16 


15.5116 


19.147 


13. 


40.8407 


132.73 


'"% 


69.5077 


384.46 


23-32 


2.25802 


.40574 


5. 


15.703) 


19.635 


% 


41.2334 


135.30 


H 


69.9004 


388.82 


H 


2.35619 


.4117J 


l-lf. 


15.9045 


20.129 


H 


41.6261 


137.S9 


Vs 


70.2931 


393.20 


25-32 2.4ot37 


.479(7 


H 


16.1037 


20.629 


Vs 


42.0188 


140.50 


H 


70.6858 


397.61 


13-16 2.55254 


.5184» 


3-16 


16.2J70 


21.135 


a 


42.4115 


143.14 


% 


71.0785 


402.04 


27-32 


2.65072 


.55JU 


'i 


16.4934 


21.648 


H 


4.'.8042 


145.80 


H 


71.4712 


406.49 


% 


2.7+889 


.60132 


5-16 


16.;)897 


22.166 


?4 


43.1969 


148.49 


y» 


71.8639 


410.97 


29-32 


2.84707 


.61501 


H 


16.8861 


22.691 


% 


43.5896 


151.20 


23. 


72.2566 


415.48 


15-16 


2.94521 


.69021) 


7-16 


17.0824 


23.221 


14. 


43.9823 


1.53.94 


% 


72.6493 


420.00 


31-32 


3.04342 


.7370S 


14 


17.2788 


23.758 


^ 


44.3750 


156.70 


Ya 


73.0420 


424.56 


1. 


3.14139 


.78510 


9-16 


17.4751 


24.301 


M 


44.7677 


159.48 


% 


73.4347 


429.13 


1-16 


3.33794 


.88661 


% 


17.6715 


24.850 


% 


45.1604 


162.30 


Yi 


73.8274 


433.74 


% 


3.53429 


.99402 


U-16 


17.8678 


25.406 


Vi 


45.5531 


165.13 


y» 


74.2201 


438.36 


3-16 


3.73064 


1.1075 


H 


18.0642 


25.967 


% 


45.9458 


167.99 


H 


74.6128 


443.01 


H 


3.92699 


1.2272 


1316 


18.2605 


26.535 


H 


46.3385 


170.87 


y» 


75.0055 


447.69 


5-16, 4.12334 


1.3530 


Vs 


18.4569 


27.109 


}s 


46.7312 


173.78 


24. 


75.3982 


452.39 


%] 4 31969 


1.4849 


15-16 


18.6532 


27.688 


15. 


47.1239 


176.71 


^ 


75.7909 


457.11 


7-16; 4.51604 


1.6230 


6. 


18.8496 


28.274 


% 


47.5166 


179.67 


H 


76.1836 


461.86 


H 4.71239 


1.7671 


H 


19.2423 


29.465 


M 


47.9093 


182.65 


Vs 


765763 


466.64 


9-16 4.90874 


1.9175 


a 


19.6350 


30.680 


% 


43.3020 


185.66 


4 


76.9690 


471.4* 


% 5.10509 


2.0739 


% 


20.0277 


31.919 


¥2 


48.6947 


188.69 


% 


77.3617 


476.26 


11-16 5.30144 


2.2385 


4 


20.4204 


33.183 


% 


49.0874 


191.75 


% 


77.7544 


431.11 


% 5.49779 


2.40.53 


H 


20.8131 


34.472 


H 


49.4801 


194.83 


y» 


78.1471 


485.98 


13-16 5.69414 


2.5802 


H 


21.2058 


35.785 


% 


49.8728 


197.93 


25. 


78.5398 


490.87 


Va 5.89049 


2.7612 


y» 


21.5984 


37.122 


16. 


50.2655 


201.06 


J^ 


78.9325 


495.79 


15-16 6.08684 


2.9483 




21.9911 


38.485 


« 


50.6582 


204.22 


% 


79.3252 


500.74 


a. : 6.28319 


3.1416 


H 


22.3838 


39.871 


H 


51.0509 


207.39 


% 


79.7179 


505.71 


1-16 6.47953 


3.3410 


''i 


22.7765 


41.282 


% 


51.4436 


210.60 


H 


80.1106 


510.71 


H 6.67588 


3.5 136 


H 


23.1692 


42.718 


Vz 


51.8363 


213.82 


% 


80.5033 


515.72 


3-16 687223 


3.7583 


14 


23.5619 


44.179 


% 


52.2290 


217 08 


H 


80.8960 


520.77 


}4 7.06858 


3.9761 


H 


23.9546 


45 664 


Vi 


52.6217 


220.35 


y» 


81.2887 


525.84 


5 16 7.26493 


4.20.)0 


% 


24.3473 


47.173 


Ve 


53.0144 


223.65 


26. 


81.6814 


530.93 


% 7.46128 


4.4301 


y» 


24.7400 


48.707 


17. 


53.4071 


226.98 


% 


82.0741 


536.05 


7-16 7.65763 


4.6664 


8. 


2.5.1327 


50.265 


H 


53.7998 


230.33 


H 


82.4668 


541.19 


}i' 7.85398 


4.90S7 


^ 


25.5254 


51.849 


a 


54.1925 


233.71 


% 


82.8595 


546.35 


9-16 8.05033 


5.1572 


H 


25 9181 


53.456 


% 


54.5852 


237.10 


14 


83.2522 


551.55 


^i 8.24668 


5.4119 


% 


26.3108 


55.088 


^ 


54.9779 


240.53 


% 


83.6449 


556.76 


11-16 8.44303 


5.6727 


H 


26.7035 


56.745 


% 


55.3706 


243.98 


% 


84.0376 


562.00 


13-lJ 


8.63938 


5.9396 


% 


27.D962 


58.426 


% 


55.7633 


247.45 


% 


84.4303 


567.27 


8.83573 


6.2126 


H 


27.4,839 


60.132 


% 


56.1560 


250.95 


27. 


84.8230 


572.56 


% 


9.03208 


6.4918 


% 


27.8816 


61.862 


18. 


56.5487 


254.47 


H 


85.2157 


577.87 


15-16 


9.22843 


6.7771 


9. 


28.2743 


63.617 


H 


56.9414 


258.02 


H 


85.6084 


583.21 


s. 


9.42478 


7.0686 


H 


28.6670 


65.397 


M 


57.3341 


261.59 


Vs 


86.0011 


588.57 


1-16 


9.62113 


7.3662 


H 


29.0597 


67.201 


% 


57.7268 


265.18 


x<. 


86.39.38 


593.96 


H 


9.81748 


7.6699 


% 


29.4524 


! 69.029 


M, 


58.1195 


268.80 


% 


86.7865 


599.37 


3-16 10.0138 


7.9798 


h 


29.8451 


i -70.882 


% 


58.5122 


272.45 


% 


87.1792 


604.81 


14 10.2102 


8.2958 


% 


.30.2378 


72.760 


H 


58.9049 


276.12 


y. 


87.5719 


610.27 


5-16 10.4065 


8.6179 


H 


30.6.305 


74 662 


% 


59.2976 


279.81 


28. 


87.9646 


615.75 


% 10.6029 . 


8.9462 


% 


31.0232 


1 76.589 


19. 


59.6903 


283.53 


% 


88.3573 


621. -26 


M6 


10.7992 


9.2306 


10. 


31.4159 


1 78.540 


% 


60.0830 


287.27 


H 


88.7500 


626.80 



170 TABLE NO. 71~C0K. 

From Trautwine's "Civil Enaineer's Pocliet Book." 



CIRCLES. 



TABI.E 1 OF CIRCIiES— (Continued). 
Diameters in units and eijirlitlis, drc. 



Diam. 


Clrcumf. 


Area. 


Diam- 


Circumf. 


Area. 


Diam. 


Circumf. 


Area. 


Diam- 


Circumf. 


Area. 


^^8 


89.1427 


632.36 


38. 


119.381 


1134.1 


i->% 


149.618 


1781.4 


57^ 


179.856 


2574.2 


^2 


89.5354 


637.94 


M 


119.773 


1141.6 


% 


150.011 


1790.8 


% 


180.249 


2585.4 


% 


89.9281 


643.55 


H 


120.166 


1149.1 


y^ 


150.404 


1800.1 


34 


180.642 


2596.7 


\ 


90.3208 


649.18 


% 


120.559 


1156.6 


48 


150.796 


1809.6 


% 


181.034 


2608.0 


% 


90.7135 


654.84 


3-2 


120.951 


1164.2 


3i 


151.189 


1819.0 


H 


181.427 


2619.4 


S9. 


91.1062 


660.52 


% 


121.344 


1171.7 


34 


151.582 


1828.5 


Vs 


181.820 


2630.7 


« 


91.4989 


666.23 


% 


121.737 


1179.3 


% 


151.975 


1837.9 


58. 


182.212 


2642.1 


M 


91.8916 


671.96 


% 


122.129 


1180.9 


1* 


152.367 


1847.5 


^ 


182.605 


2653.5 


% 


92.2843 


677.71 


39. 


122.522 


1194.6 


% 


152.760 


1857.0 


M 


182.998 


2664.9 


^ 


92.6770 


683.49 


H 


122.915 


1202.3 


H 


153.153 


1866.5 


% 


183.390 


2676.4 


% 


93.0697 


689.30 


3-4 


123.308 


1210.0 


Vs 


153.545 


1876.1 


34 


183.783 


2687.8 


% 


93.4624 


695.13 


% 


123.700 


1217.7 


49. 


153.938 


1885.7 


% 


184.176 


2699.3 


% 


93.8551 


700.98 


34 


124.093 


1225.4 


}i 


154.331 


1895.4 


H 


184.569 


2710.9 


80. 


94.2478 


706.86 


% 


124.486 


12,33.2 


34 


154.723 


1P05.0 


% 


184.961 


2722.4 


« 


94.6405 


712.76 


% 


124.878 


1241.0 


% 


155.116 


1914.7 


59. 


185.354 


2734.0 


H 


95.0332 


718.69 


% 


125.271 


1248.8 


}^ 


155.509 


1924.4 


M 


185.747 


2745.6 


% 


95.4259 


724.64 


40. 


125.664 


1256.6 


% 


155.902 


1934.2 


W 


186.139 


2757.2 


^ 


95.8186 


730.62 


3i 


1J6.056 


1264.5 


H 


156.294 


1943.9 


% 


186.532 


2768.8 


^ 


96.2113 


736.62 


?4 


126.449 


1272.4 


Vs 


156.687 


1953.7 


34 


186.925 


2780.5 


% 


96.6040 


742.64 


?8 


126.842 


1280.3 


50. 


157.080 


1963.5 


Vi 


187.317 


2792.2 


% 


96.9967 


748.69 


34 


127.235 


1288.2 


H 


157.472 


1973.3 


H 


187.710 


2803.9 


81. 


97.3894 


754.77 


% 


127.627 


1296.2 


34 


157.865 


1983.2 


Vs 


188.103 


2815.7 


H 


97.7821 


760.87 


H 


128.020 


1304.2 


% 


158.258 


1993.1 


60. 


188.496 


2827.4 


Ji 


98.1748 


766.99 


Ve 


128.413 


1312.2 


34 


158.650 


20030 


% 


188.888 


2839.2 


% 


98.5675 


773.14 


41. 


128.805 


1320.3 


% 


159.043 


2012.9 


34 


189.281 


2851.0 


^ 


98.9602 


779.31 


H 


129 198 


1328.3 


H 


159.436 


2022.8 


% 


189.674 


2862.9 


% 


99.3529 


785.51 


U 


129.591 


1336.4 


% 


159.829 


2032.8 


}4 


190.066 


2874.8 


% 


99.7456 


791.73 


% 


129.983 


1344.5 


51. 


160.221 


2042.8 


% 


190.459 


2886.6 


% 


100.138 


797.98 


3>i 


130..376 


1352 7 


H 


160.614 


2052.8 


% 


190.852 


2898.6 


32. 


100.531 


804.25 


% 


130.769 


1360.8 


M 


161.007 


2062.9 


% 


191.244 


2910.5 


H 


100.924 


810.54 


H 


131.161 


1369.0 


% 


161.399 


2073.0 


61. 


191.637 


2922.5 


M 


101.316 


816.66 


% 


1.31.554 


1377.2 


% 


161.792 


2083.1 


% 


192.030 


2934.5 


% 


101.709 


823.21 


42. 


131.947 


1385.4 


% 


162.185 


2093.2 


M 


192.423 


2946.5 


34 


102.102 


829.58 


^ 


132.340 


1393.7 


% 


162.577 


2103.3 


% 


192.815 


2958.5 


% 


102.494 


835.97 


J4 


132.732 


1402.0 


y» 


162.970 


2113.5 


14 


193.208 


2970.6 


% 


102.887 


842.39 


% 


1.33.125 


1410.3 


52. 


163.363 


2123.7 


% 


193.601 


2982.7 


y» 


103.280 


848.83 


Vi 


133.518 


1418.6 


^ 


163.756 


2133.9 


% 


193.993 


2994.8 


33. 


103.673 


855.30 


fi5 

^8 


133.910 


1427.0 


M 


164.148 


2144.2 


Ve 


194.386 


3006.9 


^ 


104.065 


861.79 


?i 


134.303 


1435.4 


% 


164.541 


2154.5 


62. 


19.4.779 


3019.1 


M 


104.458 


8§8.31 


% 


134.696 


1443.8 


H 


164.934 


2164.8 


H 


195.171 


3031.3 


% 


104.851 


874.85 


43. 


135.088 


1452.2 


% 


165.326 


2175.1 


M 


195.564 


3043.5 


34 


105.243 


881.41 


M 


135.481 


1460.7 


% 


165.719 


2185.4 


% 


195.957 


3055.7 


% 


105.636 


888.00 


34 


135.874 


1469.1 


% 


166.112 


2195.8 


Vi 


196.350 


3068.0 


?4 


106.029 


894.62 


^8 


136.267 


1477.6 


53. 


166.504 


2206.2 


% 


196.742 


3080.3 


% 


106.421 


901.26 


yk 


1.36.659 


1486.2 


Vi 


166.897 


2216.6 


H 


197.135 


3092.6 


34. 


106.814 


907.92 


% 


137.052 


1494.7 


H 


167.290 


2227.0 


% 


197.528 


3104.9 


K 


107.207 


914.61 


% 


137.445 


1503.3 


% 


167.683 


2237.5 


63. 


197.920 


3117.2 


^4 


107.600 


921.32 


% 


137.837 


1511.9 


Vi 


168.075 


2248.0 


)4 


198.313 


3129.6 


% 


107.992 


928.06 


44. 


138.230 


1520.5 


% 


168.468 


2258.5 


34 


198.706 


3142.0 


34 


108.385 


934.82 


H 


138.623 


1529.2 


% 


168.861 


2269.1 


% 


199.098 


3154.5 


^ 


108.778 


941.61 


74 


139.015 


1537.9 


Ve 


169.253 


2279.6 


Vi 


199.491 


3166.9 


?-i 


109.170 


948.42 


Vi 


139.408 


1546.6 


54. 


169.646 


2290.2 


% 


199.884 


3179.4 


K 


109.563 


955.25 


M 


139.801 


1555.3 


H 


170.039 


2300.8 


% 


200.277 


3191.9 


36. 


109.956 


962.11 


% 


140.194 


1564.0 


H 


170.431 


2311.5 


X 


200.669 


3204.4 


H 


110.348 


969.00 


% 


140 586 


1572.8 


% 


170.824 


2322.1 


64. 


201.062 


3217.0 


M 


110.741 


975.91 


% 


140.979 


1581.6 


34 


171.217 


2332.8 


H 


201.455 


3229.6 


*6 


111.134 


982.84 


45. 


141.372 


1590.4 


% 


171.609 


2343.5 


Va. 


201.847 


3242.2 


J6 


111.527 


989.80 


M 


141.764 


1599.3 


H 


172.002 


2354.3 


% 


202.240 


3254.8 


>8 


111.919 


996. 7S 


H 


142.157 


1608.2 


y» 


172.395 


2365.0 


^' 


202.633 


3267.5 


Vi 


112.312 


1003.8 


% 


142.550 


1617.0 


55. 


172.788 


2375.8 


% 


203.025 


3280.1 


% 


112.705 


1010. K 


34 


142.942 


1626.0 


Vi 


173. 180 


2386.6 


% 


203.418 


3292.8 


M. 


113.097 


1017.9 


% 


143.335 


1634.9 


Vi 


173.573 


2397.5 


% 


203.811 


3305.6 


^ 


113.490 


1025.0 


y* 


143.728 


1643.9 


% 


173.966 


2408.3 


65. 


204.204 


3318.3 


J4 


113,883 


1032 1 


% 


144.121 


1652.9 


34 


174.358 


2419.2 


M 


204.596 


3331.1 


% 


114.275 


1039.2 


46 


144.513 


1661.9 


% 


174.751 


2430.1 


M 


204.989 


3343.9 


J^ 


114.668 


1046.3 


M 


144.906 


1670.9 


Va. 


175.144 


2441.1 


% 


205.382 


3356.7 


^ 


115.061 


1053.5 


M 


145.299 


1680.0 


Vs 


175.536 


2452.0 


i4 


205.774 


3369.6 


% 


115.454 


1060.7 


y» 


145.691 


1689.1 


96. 


175.929 


2463.0 


% 


206.167 


3382.4 


?^ 


115.846 


1068 


34 


146.084 


1698.2 


H 


176.322 


2474.0 


% 


206.560 


3395.3 


87 


116.239 


1075.2 


% 


146.477 


1707.4 


H 


176.715 


2485.0 


% 


206.952 


3408.2 


% 


116.632 


1082.5 


% 


146.869 


1716.5 


% 


177.107 


2496.1 


66. 


207.345 


.3-421.2 


Vi, 


117.024 


1089.8 


% 


147.262 


1725.7 


^ 


177.500 


2507.2 


ii 


207.738 


3434.2 


% 


117.417 


1097.1 


47. 


147.6.55 


1734.9 


% 


177.893 


2518.3 


H 


208.131 


3447.2 


M. 


117.810 


1104.5 


% 


148.048 


1744.2 


H. 


178.285 


2529.4 


% 


208.523 


3460.2 


% 


118.202 


1111.8 


34 


148.440 


1753.5 


% 


178.678 


2540.6 


^ 


208.916 


3473.2 


% 


118.596 


1119.2 


% 


148.833 


1762.7 


57. 


179.071 


2551.8 


% 


209.309 


3486.3 


% 


1.18.988 


1126.7 


34 


149.226 


1772.1 


H 


179.463 


2563.0 


% 


209.701 


3499.4 



TABLE NO. 71— CON. 



171 



From Trautwiue'sj - Civil Engineer's iPocket Book.." 



CIRCLES. 



TABI.E 1 OF CIRCI.es— (Continued). 
Diameters in units and eig^taths, dee. 



Oiam. 


Ciroumf. 


Area. 


Diam. 


Circumf. 


Area. 


Diam. 


Circumf. 

i 
1 


Area. 


Diam. 


Circumf. ' 


Area. 


% 


210.094 


3512.5 


75^1 


236.405 


4447.4 


83?^ 


262.716 ' 


5492.4 


92. 


289.027 


6647.6 


67. 


210.487 


3525.7 


%' 


236.798 


4462.2 


yA 


263.108 1 


5508.8 


yi 


289.419 


6665.7 


H 


210.879 


3538.8 


)4 


237.190 


4477.0 


Vs 


263.501 , 


5525.3 


Ya 


289.812 : 


6683.8 


yi 


211.272 


3552.0 


% 


237.583 


4491.8 


84. 


263.894 


5541.8 


Ys 


290.205 


6701.9 


H 


211.66.5 


3565.2 


H 


237.976 


4506.7 


^ 


264.286 ; 


5558.3 


yi 


290.597 


6720.1 


14 


212.058 


3578.5 


y» 


238.368 


4521.5 


Ya 


264.679 ^ 


5574.8 


% 


290.990 


6738.2 


% 


212.450 


3591.7 


76. 


238.761 


4536.5 


% 


265.072 


5591.4 


Ya 


291.383 


6756.4 


H 


212.843 


3605.0 


^ 


239.154 


4551.4 


}4 


265.465 


5607.9 


Ye 


291.775 , 


6774.7 


K 


213.236 


3618.3 


Va 


239.546 


4566.4 


% 


265.857 


5624.5 


93. 


292.168 ' 


6792.9 


€8. 


213.628 


3631.7 


% 


239.939 


4581.3 


yA 


266.250 


5641.2 


yi 


292.561 ' 


681 l.i 


a 


214.021 


3645.0 


w 


240.332 


4596.3 


% 


266.643 


5657.8 


yi 


292.954 


682y.5 


u 


214.414 


3658.4 


% 


240.725 


4611.4 


85. 


267.035 ! 


5674.5 


Yb 


293.346 


6847.3 


H 


214.806 


3671.8 


K\ 


241.117 


4626.4 


% 


267.428 


5691.2 


yi 


293.739 1 


6866.1 


)4 


215.199 


3685.3 


% 


241.510 


4641.5 


H 


267.821 


5707.9 


Yi 


294.132 


6884.5 


% 


215.592 


3698.7 


77. 


241.903 


4656.6 


% 


268.213 


5724.7 


Ya 


294.524 \ 


6902.9 


% 


215.984 


3712.2 


% 


242.295 


4671.8 


Y2 


268.606 


5741.5 


y» 


294.917 


6921.3 


% 


216.377 


3725.7 


H 


242.688 


4686.9 


% 


268.999 


5758.3 


94. 


295.310 


6939.8 


69. 


216.770 


3739.3 


% 


243.0*1 


4702.1 


yA 


269..392 


5775.1 


yi 


295.702 


6958.2 


H 


217.163 


37.52.8 


)4 


243.473 


4717.3 


% 


269.784 


5791.9 


Ya 


296.095 


6976.7 


M 


217.555 


3766.4 


% 


243.866 


4732.5 


86. 


270.177 0SO8.8 i 


Ys 


296.488 


6995.3 


% 


217.948 


3780.0 


H\ 


244.259 


4747.8 


^ 


270.570 


5825.7 


yi 


296.881 


7013.8 


H 


218.341 


3793.7 


% 


244.652 


4763.1 


Ya 


270.962 


5842.6 


% 


297.273 


7032.4 


% 


218.733 


3807.3 


78. i 


245.044 


4778.4 


% 


271.355 


5859.6 


% 


297.666 


7051.0 


H 


219.126 


3821.0 


W 


245.437 


4793.7 


H 


271.748 


5876.5 


y» 


298.059 


7069.6 


K 


219.519 


3834.7 


Ya 


245.830 


4809.0 


Ys 


272.140 


5893.5 


95. 


298.451 


7088.2 


70. 


219.911 


3848.5 


%• 


246.222 


4824.4 


Ya 


272.5.33 


5910.6 


yi 


298.844 


7106.9 


^ 


220..^04 


3862.2 


^ 


246.615 


4839.8 


% 


, 272.926 


5927.6 


Ya 


299.237 


7125.6 


H 


220.697 


3876.0 


% 


247.008 


4855.2 


87. 


273.319 


5944.7 


Ys 


299.629 


7144.3 


% 


221.090 


3889.8 


H 


247.4J0O 


4870.7 


Ji 


273.711 


5961.8 


yi 


300.022 


7163.0 


)4 


221.482 


3903.6 


% 


247.793 


4886.2 


Ya 


274.104 


5978.9 


% 


300.415 


7181.8 


% 


221.875 


3917.5 


79. 


248.186 


4901.7 


Yb 


274.497 


5996.0 


Ya 


300.807 


7200.6 


y* 


222.268 


3931.4 


yi 


248.579 


4917.2 


14 


j 274.889 


6013.2 


y» 


301.200 


7219.4 


yi 


222.660 


3945.3 


}4 


248.971 


4932.7 


Yi 


275.282 


6030.4 


<J6. 


301.593 


7238.2 


71. 


223.053 


3959.2 


% 


249.364 


4948.3 


Ya 


275.675 


6047.6 


yi 


301.986 


7257.1 


H 


223.446 


3973.1 


^ 


249.757 


4963.9 


y» 


276.067 


6064.9 


Ya 


302.378 


7276 


H 


223.838 


3987.1 


% 


250.149 


4979.5 


88. 


276.460 


6082.1 


Yb 


302.771 


7294.9 


% 


224.231 


4001.1 


H 


250.542 


4995.2 


yi 


j 276.853 


6099.4 


yi 


303.164 


7313.8 


^ 


224.624 


4015.2 


y» 


250.935 


5010.9 


Ya 


277.246 


6116.7 


Y» 


303.556 


7332.8 


% 


225.017 


4029.2 


80. 


251.327 


5026.5 


Ys 


277.638 


6134.1 


Ya 


303.949 


7351.8 


% 


225.409 


4043.3 


H 


251.720 


5042.3 


14 


278.031 


6151.4 


y» 


304.342 


7370.8 


K 


225.802 


4057.4 


^ 


252.113 


5058.0 


% 


278.424 


6168.8 


97. 


304.734 


7389.8 


73. 


226.195 


4071.5 


% 


252.506 


5073.8 


Ya 


278.816 


6186.2 


H 


305.127 


7408.9 


a 


226.587 


4085.7 


3^ 


252.898 


5089.6 


% 


279.209 


6203.7 


Ya 


305.520 


7428.0 


>i 226.980 


4099.8 


% 


253.291 


5105.4 


89. 


279.602 


6221.1 


Yb 


305.913 


7447.1 


% 


227.373 


4114.0 


y* 


253.684 


5121.2 


% 


279.994 


6238.6 


yi 


306.305 


7466.2 


14 


227.765 


4128.2 


y» 


254.076 


5137.1 


Ya 


280.387 


6256.1 


% 


306.698 


7485.3 


% 


228.158 


4142.5 


81. 


254.469 


5153.0 


Y» 


280.780 


6273.7 


H 


307.091 


7504.5 


% 


228.551 


4156.8 


% 


254.862 


5168.9 


yi 


281.173 


6291.2 


y» 


307.483 


7523.7 


» 


228.944 


4171.1 


Va. 


255.254 


5184.9 


% 


281.565 


6308.8 


98. 


307.876 


7543.0 


73. 


229.336 


4185.4 


% 


255.647 


5200.8 


Ya 


281.958 


6326.4 


yi 


308.269 


7562.2 


^ 


229.729 


4199.7 


H 


256.040 


5216.8 


y» 


282.351 


6344.1 


Ya 


308.661 


7581.5 


¥< 


230.122 


4214.1 


% 


256.433 


5232.8 


90. 


282.743 


6361 .7 


Yb 


309.054 


7600.8 


% 


230.514 


4228.5 


H 


256.825 


5248.9 


yi 


283.136 


6379.4 


yi 


309.447 


7620.1 


^ 


230.907 


4242.9 


% 


257.218 


5264.9 


Ya 


283.529 


6397.1 


% 


309.840 


7639.5 


H 


231. .300 


4257.4 


82. 


257.611 


5281.0 


fi 


1 283.921 


6414.9 


H 


310.232 


7658.9 


y* 


231.692 


4271.8 


^ 


258.003 


5297.1 


3* 


! 284.314 


6432.6 


y» 


310.625 


7678.3 


% 


232.085 


4286.3 


Ya 


258.396 


5313.3 


% 


284.707 


6450.4 


99. 


311.018 


7697.7 


74. 


232.478 


4300.8 


% 


258.789 


5329.4 


Ya 


285.100 


6468.2 


yi 


311.410 


7717.1 


H 


232.871 


4315.4 


yi 


259.181 


5345.6 


% 


285.492 


6486.0 


Va 


311.803 


7736.6 


Va 


233.263 


4329.9 


% 


259.574 


5361.8 


91. 


285.885 


6503.9 


Yb 


312.196 


7756.1 


% 


233.656 


4344.5 


% 


259.967 


5378.1 


yi 


286.278 


6521.8 


yi 


312.588 


7775.6 


Ji 


234.049 


4359.2 


% 


260.359 


5394.3 


Ya 


( 286.670 


6539.7 


% 


312.981 


7795.2 


5< 


234.441 


4373.8 


83. 


260.752 


5410.6 


% 


287.063 


6557.6 


% 


313.374 


7814.8 


% 


234.834 


4388.5 


H 


261.145 


5426.9 


yi 


287.456 


6575.5 


Yb 


313.767 


7834.4 


% 


235.227 


4403.1 


Ya 


261.538 


5443.3 


% 


287.848 


6593.5 


100. 


314.159 


78&i.Q 


75. 


235.619 


4417.9 


% 


261.930 


5459.6 


Ya 


288.241 


6611.5 








H 


236.012 


4432.6 


% 


262.323 


5476.0 


% 


288.634 


6629.6 









172 TABLE NO. 72. 

From Traiitwine's "Civil Engineer's PocRet Book.' 

CIRCLES. 



TABI.E 2 OF CIRCIiES. 
Diameters in units and tenths. 



Dia. 


Circumf. 


Area. 


Dia. 


Circumf. 


Area. 


Dia. 


Circumf. 


Area. 


0.1 


.314159 


.007854 


6.3 


19.79203 


31.17245 


12.5 


39.26991 


122.7185 


.2 


.628319 


.031416 


.4 


20.10619 


32.16991 


.6 


39.58407 


124.6898 


.3 


.942478 


.070686 


.5 


20.42035 


83.18307 


.7 


39.89823 


126.6769 


A 


1.256687 


.125664 


.6 


20.73451 


34.21194 


.8 


40.21239 


128.6796 


.5 


1.570796 


.196350 


.7 


21.04867 


35.25652 


.9 


40.52655 


130.6981 


.6 


1.884956 


.282743 


.8 


21.36283 


36.31681 


13.0 


40.84070 


132.7323 


.7 


2.199115 


.384845 


.9 


21.67699 


37.39281 


.1 


41.15486 


134.7822 


.8 


2.513274 


.502655 


7.0 


21.99115 


38.48451 


.2 


41.46902 


136.8478 


.9 


2.827433 


.636173 


.1 


22.30531 


39.59192 


.3 


41.78318 


138.9291 


1.0 


3.141593 


.785398 


.2 


22.61947 


40.71504 


A 


42.09734 


141.0261 


.1 


3.455752 


.950332 


.3 


22.93363 


41.85387 


.5 


42.41150 


143.1388 


.2 


3.769911 


1.13097 


.4 


23.24779 


43.00840 


.6 


42.72566 


145.2672 


.3 


4.084070 


1.. 32732 


.5 


23.56194 


44.17865 


.7 


43.03982 


147.4114 


.4 


4.398230 


1.53938 


.6 


23.87610 


45.36460 


.8 


43.35398 


149.5712 


.5 


4.712389 


1.76715 


.7 


24.19026 


46.56626 


.9 


43.66814 


151.7468 


.6 


5.026548 


2.01062 


.8 


24.50442 


47.78362 


14.0 


43.98280 


153.9380 


.7 


5.340708 


2.26980 


.9 


24.81858 


49.01670 


.1 


44.29646 


156.1450 


.8 


5.654867 


2.54469 


8.0 


25.13274 


.50.26548 


.2 


44.61062 


158.3677 


.9 


5.969026 


2.83529 


.1 


25.44690 


51.52997 


.3 


44.92477 


160.6061 


2.0 


6.283185 


3.14159 


.2 


25.76106 


52.81017 


.4 


45.23893 


162.8602 


.1 


6.597345 


3.46361 


.3 


26.07522 


54.10608 


.5 


45.55309 


165.1300 


.2 


6.911504 


3.80133 


.4 


26.38938 


55.41769 


.6 


45.86725 


167.4155 


.3 


7.225663 


4.15476 


.5 


26.70354 


56.74502 


.7 


46.18141 


169.7167 


.4 


7.539822 


4.52389 


.6 


27.01770 


58.08805 


.8 


46.49557 


172.0336 


.5 


7.853982 


4.90874 


.7 


27.33186 


59.44679 


.9 


46.80973 


174.3662 


.6 


8.168141 


5.30929 


.8 


27.64602 


60.82123 


15.0 


47.12389 


176.7146 


.7 


8.482300 


5.72555 


.9 


27.96017 


62.21139 


.1 


47.43805 


179.0786 


.8 


8.796459 


6.15752 


9.0 


28.27433 


63.61725 


2 


47.75221 


181.4584 


.9 


9.110619 


6.60520 


.1 


28.58849 


65.03882 


'.S 


48.06637 


183.8539 


3.0 


9.424778 


7.06858 


.2 


28.90265 


66.47610 


A 


48.38053 


186.2650 


.1 


9.738937 


7.54768 


.3 


29.21681 


67.92909 


.5 


48.69469 


188.6919 


.2 


10.05310 


8.04248 


.4 


29.53097 


69.39778 


.6 


49.00885 


191.1345 


.3 


10.36726 


8.55299 


.5 


29.84513 


70.88218 


.7 


49.32300 


1935928 


.4 


10.68142 


9.07920 


.6 


30.15929 


72.38229 


.8 


49.63716 


196.0668 


.5 


10.99557 


9.62113 


.7 


30.47345 


73.89811 


.9 


49.95132 


198.5565 


.6 


11.30973 


10.17876 


.8 


30.78761 


75.42964 


16.0 


50.26548 


201.0619 


.7 


11.62389 


10.75210 


.9 


31.10177 


76.97687 


.1 


50.57964 


203.5831 


.8 


11.93805 


11.34115 


10.0 


31.41593 


78.53982 


.2 


50.89380 


206.1199 


.9 


12.25221 


11.94591 


.1 


31.73009 


80.11847 


.3 


51.20796 


208.6724 


4.0 


12.56637 


12.56637 


.2 


32.04425 


81.71282 


.4 


51.52212 


211.2407 


.1 


12.88053 


13.20254 


.3 


32.35840 


83.32289 


.5 


51.83628 


213.8246 


.2 


13.19469 


13.85442 


.4 


32.67256 


84.94867 


.6 


52.15044 


216.4243 


.3 


13.50885 


14.52201 


.5 


32.98672 


86.59015 


.7 


52.46460 


219.0397 


.4 


13.82301 


15.20531 


.6 


33.30088 


88.24734 


.8 


52.77876 


221.6708 


.5 


14.13717 


15.90431 


.7 


33.61504 


89.92024 


.9 


53.09292 


224.3176 


.6 


14.45133 


16.61903 


.8 


33.92920 


91.60884 


17.0 


53.40708 


226.9801 


.7 


14.76549 


17.34945 


.9 


:34.24336 


93.31316 


.1 


53.72123 


229.6583 


.8 


15.07964 


18.09557 


11.0 


34.55752 


95.03318 


.2 


54.03539 


232.3522 


.9 


15.39380 


18.85741 


.1 


34.87168 


96.76891 


.3 


54.34955 


235.0618 


5.0 


15.70796 


19.63495 


.2 


35.18584 


98.52035 


A 


54.66371 


237.7871 


.1 


16.02212 


20.42821 


.3 


35.50000 


100.2875 


.5 


54.97787 


240.5282 


.2 


16.33628 


21.23717 


.4 


35.81416 


102.0703 


.6 


55.29203 


243.2849 


.3 


16.65044 


22.06183 


.5 


36.12832 


103.8689 


.7 


55.60619 


246.0574 


.4 


16.96460 


22.90221 


.6 


36.44247 


105.6832 


.8 


55.92085 


248.8456 


.5 


17.27876 


23.75829 


.7 


36.75663 


107.5132 


.9 


56.23451 


2.51.6494 


.6 


17.59292 


24.63009 


.8 


37.07079 


109.3588 


18.0 


56.54867 


254.4690 


.7 


17.90708 


25.51759 


.9 


37.38495 


111.2202 


.1 


56.86283 


257.3043 


.8 


18.22124 


26.42079 


12.0 


37.69911 


113.0973 


.2 


57.17699 


260.1553 


.9 


18.53540 


27.33971 


.1 


38.01327 


114.9901 


.3 


57.49115 


268.0220 


e,o 


18.84956 


28.27433 


.2 


38.32743 


116.8987 


.4 


57.80530 


265.9044 


.1 


19.16372 


29.22467 


.3 


88.64159 


118.8229 


.5 


58.11946 


268.8025 


.2 


19.47787 


30.19071 


.4 


38.95575 


120.7628 


.6 


58.43362 


271.7163 



TAJtJl^J^ JNU. 7^— (JUJN. 173 

From Trautwine's "Civil Eng^ineer's Pocket Book." 

CIRCLES. 



TABLE 2 OF CIRCI.es— (Continued). 
I>iaineter«« in units and tenth««. 



Dia. 


Circuinf. 


Area. 


Dia. 


Circunif. 


Area. 


Dia. 


Circunif. 


Area. 


18.7 


58.74778 


274.&459 


24.9 


78.22566 


486.9547 


31.1 


97.70353 


759.6450 


.8 


59.06194 


277.5911 


25.0 


78.53982 


490.8739 


2 


98.01769 


764.6380 


.9 


59.37610 


280.5521 


.1 


78.85398 


494.8087 


'.3 


98.3318;5 


769.4467 


19.0 


59.69026 


283.5287 





79.16813 


498.7592 


.4 


98.64601 


774.3712 


.1 


60.00442 


286.5211 


'.3 


79.48229 


502.7255 


.5 


98.96017 


779.3113 


2 


60.318.58 


289.5292 


.4 


79.79645 


506.7075 


.6 


99.27433 


784.2672 


.3 


60.63274 


292.5530 


.5 


80.11061 


510.7052 


.7 


99.58849 


789.2388 


.4 


60.94690 


295.5925 


.6 


80.42477 


514.7185 


.8 


99.90265 


794.2260 


.5 


61.26106 


298.6477 


.7 


80 73893 


518.7476 


.9 


100.2168 


799.2290 


.6 


61.57522 


301.7186 


.8 


81 .05309 


522.7924 


32.0 


100.5310 


804.2477 


.7 


61.88938 


304.8052 


.9 


81.36725 


526.8529 


.1 


100.8451 


809.2821 


.8 


62.20353 


307.9075 


26.0 


81.68141 


530.9292 


.2 


101.1593 


814.3322 


.9 


62.51769 


311.0255 


.1 


81.99557 


535.0211 


.3 


101.4734 


819.3980 


20.0 


62.83185 


314.1593 


.2 


82.30973 


539.1287 


.4 


101.7876 


824.4796 


.1 


63.14601 


317.3087 


.3 


82.62389 


543.2521 


.6 


102.1018 


829.5768 


.2 


63.46017 


320.4739 


.4 


82.93805 


647.3911 


.6 


102.4159 


834.6898 


^S 


63.77433 


323.6.547 


.5 


83.2.-^/221 


651. .5459 


.7 


102.7301 


839.8184 


.4 


64.08849 


326.8513 


.6 


83.56636 


565.7163 


.8 


103.0442 


844.9628 


.5i 


64.40265 , 


330.0636 


•7 


83.88052 


559.9025 


.9 


103.3584 


850.1228 


.6 


64.71681 


333.2916 


.8 


84.19468 


564.1044 


33.0 


103.6726 


855.2986 


.7' 


65.03097 ' 


336.5353 


.9 


84.50884 


568.3220 


.1 


103.9867 


860.4901 


.8 


65.34513 


339.7947 


27.0 


84.82300 


672.6553 


.2 


104.3009 


865.6973 


.9 


65.6.5929 


343.0698 


.1 


85.13716 


676.8043 


.3 


104.6150 


870.9202 


21.0 


65.97345 


346.3606 


.2 


85.45132 


581.0690 


.4 


104.9292 


876.1588 


.1 


66.28760 


349.6671 


.3 


85.76548 


685.3494 


.5 


105.2434 


881.4131 


.2 


66.60176 


352.9894 


.4 


86.07964 


689.6455 


.6 


105.5575 


886.6831 


.3 


66.91592 


356.3273 


.5 


86.39380 


593.9574 


.7 


105.8717 


891.9688 


.4 


67.23008 


359.6809 


.6 


86.70796 


598.2849 


.8 


106.1858 


897.2703 


.5, 


67.54424 


363.0503 


.7 


87.02212 


602.6282 


.9 


106.5000 


902.5874 


.6 


67.85840 


366.4354 


.8 


87.33628 


606.9871 


34.0 


106.8142 


907.9203 


.7 


68.17256 


369.8361 


.9 


87.65044 


611.3618 


.1 


107.1283 


913,2688 


.8 


68.48672 


373.2526 


28.0 


87.96459 


615.7522 


.2 


107.4426 


918.6331 


.9 


68.80088 


376.6848 


.1 


88.27875 


620.1582 


.3 


107.7566 


924.0131 


22.0 


69.11504 


380.1327 


.2 


88.59291 


624.5800 


.4 


108.0708 


929.4088 


.1 


69.42920 


383.5963 


.3 


88.90707 


629.0175 


.6 


108.3849 


934.8202 


.2 


69.74336 


387.0756 


.4 


89.22123 


633.4707 


.6 


108.6991 


940.2473 


.3 


70.05752 


390.5707 


.5 


89.53539 


637.9397 


.7 


109.0133 


945.6901 


.4 


70.37168 


394.0814 


.6 


89.84955 


642.4243 


.8 


109.3274 


951.1486 


.5 


70.68583 


397.6078 


.7 


90.16371 


646.9246 


.9 


109.6416 


956.6228 


.6 


70.99999 


401.1500 


.8 


90.47787 


651.4407 


35.0 


109.9557 


962.1128 


.7 


71.31415 


404.7078 


.9 


90.79203 


655.9724 


.1 


110.2699 


967.6184 


.8 


71.62831 


408.2814 


29.0 


91.10619 


660;5199 


.2 


110.5841 


973.1397 


.9 


71.94247 


411.8707 


.1 


91.42035 


665.0830 


.3 


110.8982 


978.6768 


23.0 


72.25663 


415.4756 


.2 


91.73451 


669.6619 


.4 


111.2124 


984.2296 


.1 


72.57079 


419.0963 


.3 


92.04866 


674.2565 


.5 


111.5265 


989.7980 


.2 


72.88495 


422.7327 


.4 


92.36282 


678.8668 


.6 


111.8407 


995.3822 


,3 


73.19911 


426.3848 


.5 


92.67698 


683.4928 


.7 


112.1549 


1000.9821 


.4 


73.51327 


430.0526 


.6 


92.99114 


688.1345 


.8 


112.4690 


1006.5977 


.5 


73.82743 


433.7361 


.7 


93.30530 


692.7919 


.9 


112.7832 


1012.2290 


.6 


74.14159 


437.4354 


.8 


93.61946 


697.4650 


36.0 


113.0973 


1017.8760 


.7 


74.45575 


441.1503 


.9 


93.93362 


702.1538 


.1 


113.4115 


1023.5387 


.8 


74.76991 


444.8809 


30.0 


94.24778 


706.8583 


.2 


113.7257 


1029.2172 


.9 


75.08406 


448.6273 


.1 


94.56194 


711.5786 


.3 


114.0398 


1034.9113 


24.0 


75.39822 


452.3893 


.2 


94.87610 


716.3145 


.4 


114.3640 


1040.6212 


.1 


75.71238 


456.1671 


.3 


95.19026 


721.0662 


.5 


114.6681 


1046.3467 


.2 


76.02654 


459.9606 


.4 


95.50442 


725.8336 


.6 


114.9823 


1052.0880 


.3 


76.34070 


463.7698 


.5 


95.818.58 


730.6166 


.7 


115.2965 


1057.8449 


.4 


76.65486 


467.5947 


•S 


96.13274 


735.4154 


.8 


116.6106 


1063.6176 


.5 


76.96902 


471.4352 


.'? 


96.44689 


740.2299 


.9 


116.9248 


1069.4060 


.6 


77.28318 


475.2916 


.8 


96.76105 


745.0601 


37.0 


116.2389 


1075.2101 


.7 


77.59734 


479.1636 


.9 


97.07521 


749.9060 


.1 


116.5531 


1081.0299 


.8 


77.91150 


483.0513 


31.0 


97.38937 


764.7676 


.2 


116.8672 


1086.8654 



174 TABLE NO. 72— CON. 

From Tratitwine's "Civil Engineer's Pocket Book." 



CIRCLES. . 



TABL.I: 2 OF CIRCIiES— (Continued). 
Diameters in units and tenths. 



Dia. 


Circuiuf. 


Area. 


Dia. 


Circumf. 


Area. 


Dia. 


Circumf. 


Area. 


37.3 


117.1814 


1092.7166 


43.5 


136.6593 


1486.1697 


49.7 


156.1372 


1940.0041 


.4 


117.4956 


1098.5835 


.6 


136.9734 


1493.0105 


.8 


156.4513 


1947.8189 


.5 


117.8097 


1104.4662 


.7 


137.2876 


1499.8670 


.9 


156.7655 


1955.6493 


.6 


118.1239 


1110.3645 


.8 


137.6018 


1506.7393 


50.0 


157.0796 


1963.4954 


.7 


118.4380 


1116.2786 


.9 


137.9159 


1513.6272 


.1 


157.3938 


1971.3572 


.8 


118.7522 


1122.2083 


44.0 


138.2301 


1520.5308 


.2 


157.7080 


1979.2348 


.9 


119.0664 


1128.1538 


.1 


138.5442 


1527.4502 


.3 


158.0221 


1987.1280 


38.0 


119.3805 


1134.1149 


.2 


138.8584 


1534.3853 


.4 


158.3363 


1995.0370 


.1 


119.6947 


1140.0918 


.3 


139.1726 


1541.3360 


.5 


158.6504 


2002.9617 


.2 


120.0088 


1146.0844 


.4 


139.4867 


1.548.3025 


.6 


158.9646 


2010.9020 


.3 


120.3280 


1152.0927 


.5 


139.8009 


1555.2847 


.7 


159.2787 


2018.8581 


.4 


120.6372 


1158.1167 


.6 


140.1150 


1562.2826 


.8 


159.5929 


2026.8299 


.5 


120.9513 


1164.1564 


.7 


140.4292 


1569.2962 


.9 


159.9071 


2034.8174 


.6 


121.2655 


1170.2118 


.8 


140.7434 


1576.3255 


51.0 


160.2212 


2042.8206 


.7 


121.5796 


1176.2830 


.9 


141.0575 


1583.3706 


.1 


160.5354 


2050.8395 


.8 


121.8938 


1182.3698 


45.0 


141.3717 


1590.4313 


.2 


160.8495 


2058.8742 


.9 


122.2080 


1188.4724 


.1 


141.6858 


1597.5077 


.3 


161.1637 


2066.9245 


39.0 


122.5221 


1194.5906 


.2 


142.0000 


1604.-5999 


.4 


161.4779 


2074.9905 


.1 


122.8363 


1200.7246 


.3 


142.3141 


1611.7077 


.5 


161.7920 


2083.0723 


.2 


123.1504 


1206.8742 


.4 


142.6283 


1618.8313 


.6 


162.1062 


2091.1697 


.3 


123.4646 


1213.0396 


.5 


142.9425 


1625.9705 


.7 


162.4203 


2099.2829 


.4 


123.7788 


1219.2207 


.6 


143.2566 


1633.1255 


.8 


162.7345 


2107.4118 


.5 


124.0929 


1225.4175 


.7 


143.5708 


1640.2962 


.9 


163.0487 


2115.5563 


.6 


124.4071 


1231.6300 


.8 


143.8849 


1647.4826 


52.0 


163.3628 


2123.7166 


.7 


124.7212 


1237.8582 


.9 


144.1991 


1654.6847 


.1 


163.6770 


2131.8926 


.8 


125.0354 


1244.1021 


46.0 


144.5133 


1661.9025 


.2 


163.9911 


2140.0843 


.9 


125.3495 


1250.3617 


.1 


144.8274 


1669.1360 


.3 


164.3053 


2148.2917 


40.0 


125.6637 


1256.6371 


.2 


145.1416 


1676.8853 


.4 


164.6195 


2156.5149 


.1 


125.9779 


1262.9281 


.3 


145.4557 


1683.6502 


.5 


164.9336 


2164.7537 


-2 


126.2920 


1269.2348 


.4 


145.7699 


1690.9308 


.6 


165.2478 


2173.0082 


.3 


126.6062 


1275..5573 


.5 


146.0841 


1698.2272 


.7 


165.5619 


2181.2785 


.4 


126.9203 


1281.8955 


.6 


146.3982 


1705.5392 


.8 


165.8761 


2189.5644 


.5 


127.2345 


1288.2493 


.7 1 146.7124 


1712.8670 


.9 


166.1903 


2197.8661 


.6 


127.5487 


1294.6189 


.8 


147.0265 


1720.2105 


53.0 


166.5044 


2206.1834 


.7 


127.8628 


1301.0042 


.9 


147.3407 


1727.5697 


.1 


166.8186 


2214.5165 


.8 


128.1770 


1307.4052 


47.0 


147.6549 


1734.9445 


.2 


167.1327 


2222.86.53 


.9 


128.4911 


1313.8219 


.1 


147.9690 


1742.3351 


.3 


167.4469 


2231.2298 


41.0 


128.8053 


1320.2543 


.2 


148.2832 


1749.7414 


.4 


167.7610 


2239.6100 


.1 


129.1195 


1326.7024 


.3 


148.5973 


1757.1635 


.5 


168.0752 


2248.0059 


.2 


129.4336 


1333.1663 


.4 


148.9115 


1764.6012 


.6 


168.3894 


2256.4175 


.3 


129.7478 


1339.6458 


.5 


149.2257 


1772.0546 


.7 


168.7035 


2264.8448 


.4 


130.0619 


1346.1410 


.6 


149.5398 


1779.5237 


.8 


169.0177 


2273.2879 


.5 


130.3761 


1352.6520 


.7 


149.8.540 


1787.0086 


.9 


169.3318 


2281.7466 


.6 


130.6903 


1359.1786 


.8 


150.1681 


1794.5091 


54.0 


169.6460 


2290.2210 


.7 


131.0044 


1365.7210 


.9 


150.4823 


1802.0254 


.1 


169.9602 


2298.7112 


.8 


131.3186 


1372.2791 


48.0 


150.7961 


1809.5574 


.2 


170,2743 


2307.2171 


.9 


131.6327 


1378.8.529 


.1 


151.1106 


1817.1050 


.3 


170.5885 


2315.7386 


42.0 


131.9469 


1385.4424 


.2 


151.4248 


1824.6684 


.4 


170.9026 


2324.2759 


.1 


132.2611 


1392.0476 


.3 


151.7389 


1832.2475 


.5 


171.2168 


2332.8289 


.2 


132.5752 


1398.6685 


.4 


152.0531 


1839.8423 


.6 


171.5310 


2341.3976 


.3 


132.8894 


1405.3051 


.5 


152.3672 


1847.4528 


.7 


171.8451 


2349.9820 


.4 


133.2035 


1411.9574 


.6 


152.6814 


1855.0790 


.8 


172.1593 


2358.5821 


.5 


133.5177 


1418.6254 


.7 


152.9956 


1862.7210 


.9 


172.4734 


2367.1979 


.6 


133.8318 


1425.3092 


.8 


153.3097 


1870.3786 


56.0 


172.7876 


2375.8294 


.7 


134.1460 


1432.0086 


.9 


153.6239 


1878.0519 


.1 


173.1018 


2384.4767 


.8 


134.4602 


1438.7238 


49.0 


153.9380 


1885.7410 


.2 


173.4159 


2393.1396 


.9 


134.7743 


1445.4546 


.1 


154.2522 


1893.4457 


.3 


173.7301 


2401.8183 


43.0 


135.0885 


1452.2012 


.2 


154.5664 


1901.1662 


.4 


174.0442 


2410.5126 


.1 


135.4026 


1458.9635 


.3 


154.8805 


1908.9024 


.5 


174.3584 


2419.2227 


.2 


135.7168 


1465.7415 


.4 


155.1947 


1916.6543 


.6 


174.6726 


2427.9485 


.3 


136.0310 


1472.5352 


.5 


155.5088 


1924.4218 


.7 


174.9867 


2436.6899 


.4 


136.3451 


1479.3446 


.6 


155.8230 


1932.-2051 


.8 


175.3009 


2445.4471 



TABLE NO. 72— CON. 175 

From Trautwine's "Civil Engineer*** Pocket Book.'' 

CIRCLES. 



TABIiE 2 OF CIRCXES— (Continued). 
Diameters in units and tenths. 



Dia. 


Circumf. 


Area. 


Dia. 


Circumf. 


Area. 

3028.8173 


Dia. 

68.3 


Circumf. 


Area. 


55.9 


175.6150 


24r>4.2200 


62.1 


195.0929 


214.5708 


3663.7960 


66.0 


175.9292 


2463.U086 


.2 


195.4071 


3038.5798 


.4 


214.8849 


3674.5324 


.1 


176.2433 


2471.8130 


.3 


195.7212 


3048.3580 


.5 


215.1991 


3685.2845 


.2 


176.5575 


248*1.6330 


.4 


196.0354 


3058.1520 


.6 


215.5133 


3696.0523 


.3 


176.8717 


2489.4687 


.5 


196.3495 


3067.9616 


.7 


215.8274 


3706.8359 


A 


177.1858 


2498.3201 


.6 


196.6637 


3077.7869 


.8 


216.1416 


3717.6351 


.5 


177.5000 


2.507.1873 


.7 


196.9779 


3087.6279 


.9 


216.4557 


3728.4500 


.6 


177.8141 


2516.0701 


.8 


197.2920 


3097.4847 


69.0 


216.7699 


3739.2807 


.7 


178.1283 


2524.9687 


.9 


197.6062 


3107.3571 


.1 


217.0841 


3750.1270 


.8 


178.4425 


2533.8830 


63.0 


197.9203 


3117.2453 


.2 


217.3982 


3760.9891 


.9 


178.7566 


2542.8129 


.1 


198.2345 


3127.1492 


.3 


217.7124 


3771.8668 


67.0 


179.0708 


2.551.7586 


.2 


198.5487 


3137.0688 


.4 


218.0265 


3782.7603 


.1 


179.3849 


2560.7200 


.3 


198.8628 


3147.0040 


.5 


218.3407 


3793.6695 


.2 


179.6991 


2.569.6971 


.4 


199.1770 


3156.9550 


.6 


218.6548 


3804.5944 


.3 


180.0133 


2578.6899 


.5 


199.4911 


3166.9217 


.7 


218.9690 


3815.5350 


.4 


180.3274 


2587.6985 


.6 


199.8053 


3176.9042 


.8 


219.2832 


3826.4913 


.5 


180.6416 


2596.7227 


.7 


200.1195 


3186.9023 


.9 


219.5973 


3837.4633 


.6 


180.9557 


2605.7626 


.8 


200.43.36 


3196.9161 


70.0 


219.9115 


3848.4510 


.7 


181.2699 


2614.8183 


.9 


200.7478 


3206.9456 


.1 


220.2256 


3859.4544 


.8 


181.5841 


2623.8896 


64.0 


201.0619 


3216.9909 


.2 


220.5398 


3870.4736 


.9 


181.8982 


2632.9767 


.1 


201.3761 


3227.0518 


.3 


220.8540 


3881.5084 


58.0 


182.2124 


2642.0794 


.2 


201.6902 


3237.1285 


.4 


221.1681 


3892.5590 


.1 


182.5265 


2651.1979 


.3 


202.0044 


3247.2209 


.5 


221.4823 


3903.6252 


.2 


182.8407 


2660.3321 


.4 


202.3186 


32.57.3289 


.6 


221.7964 


3914.7072 


.3 


183.1.549 


2669.4820 


.5 


202.6327 


3267.4527 


•7 


222.1106 


3925.8049 


A 


183.4690 


2678.6476 


.6 


202.9469 


3277.5922 


.8 


222.4218 


3936.9182 


.5 


183.7832 


2687.8289 


.7 


203.2610 


3287.7474 


.9 


222.7389 


3948.0473 


.6 


184.0973 


2697.02.59 


.8 


203.5752 


3297.9183 


71.0 


223.0531 


39.59.1921 


.7 


1&4.4115 


2706.2386 


.9 


203.8894 


3308.1049 


.1 


223.3672 


3970.3526 


.8 


184.7256 


2715.4670 


65.0 


204.2035 


3318.3072 


.2 


223.6814 


3981.5289 


.9 


185.0398 


2724.7112 


.1 


204.5177 


3328.5253 


.3 


223.9956 


3992.7208 


59.0 


185.3540 


2733.9710 


.2 


204.8318 


3338.7590 


.4 


224.3097 


4003.9284 


.1 


18.5.6681 


2743.2466 


.3 


205.1460 


3349.0085 


.5 


224.6239 


4015.1518 


.2 


185.9823 


2752.5378 


.4 


205.4602 


3359.2736 


.6 


224.9380 


4026.3908 


.3 


186.2964 


2761.8448 


.5 


205.7743 


3369.5545 


.7 


225.2522 


4037.6456 


.4 


186.6106 


2771.1675 


.6 


206.0885 


3379.8510 


.8 


225.5664 


4048.9160 


.6 


186.9248 


2780.5058 


.7 


206.4026 


3390.1633 


.9 


225,8805 


4060.2022 


.6 


187.2389 


2789.8599 


.8 


206 7168 


3400.4913 


72.0 


226.1947 


4071.5041 


.7 


187.5531 


2799.2297 


.9 


207.0310 


3410.8350 


.1 


226.5088 


4082.8217 


.8 


187.8672 


2808.6152 


66.0 


207.3451 


3421.1944 


.2 


226.8230 


4094.1.550 


.9 


188.1814 


2818.0165 


.1 


207.6593 


3431.5695 


.3 


227.1371 


4105.5040 


60.0 


188.4956 


2827.4334 


.2 


207.9734 


3441.9603 


.4 


227.4513 


4116.8687 


.1 


188.8097 


28.36.8660 


.3 


208.2876 


3452.3669 


.5 


227.7655 


4128.2491 


.2 


189.1239 


2846.3144 


.4 


208.6018 


3462.7891 


.6 


228.0796 


4139.6452 


.3 


189.4380 


2&55.7784 


.5 


208.91.59 


3473.2270 


.7 


228.3938 


4151.0571 


.4 


189.7522 


2865.2582 


.6 


209.2301 


3483.6807 


.8 


228.7079 


4162.4846 


.5 


190.0664 


2874.7536 


.7 


209.5442 


3494.1500 


.9 


229.0221 


4173.9279 


.6 


190.3805 


2884.2648 


.8 


209.8.584 


3504.6351 


73.0 


229.3363 


4185.3868 


.7 


190.6947 


2893.7917 


.9 


210.1725 


3515.1359 


.1 


229.6504 


4196.8615 


.8 


191.0088 


2903.3343 


67.0 


210.4867 


3525.6524 


.2 


229.9646 


4208.3519 


.9 


191.3230 


2912.8926 


.1 


210.8009 1 


3536.1845 


.3 


230.2787 


4219.8579 


61.0 


191.6372 


2922.4666 


.2 


211.1150 


3.546.7324 


.4 


230.5929 


4231.3797 


.1 


191.9513 


2932.0563 


.3 


211.4292 


3557.2960 


.5 


230.9071 


4242.9172 


.2 


192.26.55 


2941.6617 


.4 


211.7433 


3567.8754 


.6 


231.2212 


4254.4704 


.3 


192.5796 


2951.2828 


.5 1 


212.0575 


3.578.4704 


.7 


231.5354 


4266.0394 


.4 


192.8938 


2960.9197 


.6' 


212.3717 


3.589.0811 


.8 


231.8495 


4277.6240 


.5 


193.2079 


2970..5722 


,7 


212.6858 


3599.7075 


.9 


232.1637 


4289.2243 


.6 


193..5221 


2980.2405 


.8 


213.0000 1 


.3610.3497 


74.0 


232.4779 


4;?00.8403 


.7 


193.8363 


2989.9244 


.9 


213.3141 


3621.0075 


.1 


232.7920 


4312.4721 


.8 


194.1504 


2999.6241 


68.0 


213.6283 


3631.6811 


o 


2.33.1062 


4324.1195 


.9 


194.4646 


3009.3395 


.1 


213.9425 


3642.3704 


'.Z 


233.4203 1 


4335.7827 


690 


194.7787 


3m9.f)705 


.2 1 


214.2.566 


3653.0754 


A 


233.7345 i 


4347.4616 



176 TABLE NO. 72— CON. 

From Traut wine's "Civil £iig'iiieer's Pocket Boole. 



CIRCLES. 



TABLE 2 OF C'lRCJLES— (Continued). 
Biameters in units and tenths. 



Dia. 


Circumf. 


Area. 


Dia. 

80.7 


Circumf, 


Area. 


Dia. 

86.9 


Circumf. 


Area. 


74.5 


234.0487 


4359.1562 


253.5265 


5114.8977 


273.0044 


5931.0206 


.6 


234.3628 


4370.8664 


.8 


253.8407 


5127.5819 


87.0 


273.3186 


5944.6787 


.7 


234.6770 


4382.5924 


.9 


254.1548 


5140.2818 


.1 


273.6327 


5958.3525 


.8 


2.-4.9911 


439-1.3341 


81.0 


^54.4690 


5152.9974 


2 


273.9469 


5972.0420 


.9 


235.3053 


4406.0916 


.1 


254.7832 


5165.7287 


.3 


274.2610 


5985.7472 


75.0 


235.6194 


4417.8647 


.2 


255.0973 


5178.4757 


.4 


274.5752 


5999.4681 


.1 


235.9336 


4429.65a5 


.3 


255.4115 


5191.2384 


.5 


274.8894 


6013.2047 


.2 


236.2478 


4441.4580 


.4 


255.7256 


5204.0168 


.6 


275.2035 


6026.9570 


.3 


236.5619 


4453.2783 


.5 


256.0398 


5216.8110 


.7 


275.5177 


6040.7250 


.4 


236.8761 


4465.1142 


.6 


256.3540 


5229.6208 


.8 


275.8318 


6054.5088 


.5 


237.1902 


4476.9659 


.7 


256.6681 


5242.4463 


.9 


276.1460 


6068.3082 


.6 


237.5044 


4488 8332 


.8 


256.9823 


5255.2876 


88.0 


276.4602 


6082.1234 


.7 


237.8186 


4500.7163 


.9 


257.2964 


5268.1446 


.1 


276.7743 


6095.9542 


.8 


238.1327 


4512.6151 


82.0 


257.6106 


5281.0173 


.2 


277.0885 


6109.8008 


.9 


238.4469 


4524.5296 


.1 


257.9248 


5293.9056 


.3 


277.4026 


6123.6631 


76.0 238.7610 


4536.4598 


2 


258.2889 


5306.8097 


.4 


277.7168 


6137.5411 


.1 239.0752 


4548.4057 


^3 


258.5531 


5319.7295 


.5 


278.0309 


6151.4348 


.2 : 239.3894 


1560.3673 


.4 


258.8672 


5332.66n0 


.6 278.3451 


6165.3142 


.3 239.7035 


4572.3446 


.5 


259.1814 


5345.6162 


.7 278.6593 


6179.2693 


.4 240.0177 


4584.3377 


.6 


259.4956 


5358.5832 


.8 278.9734 


6193.2101 


.5 240.3318 


4596.3464 


.7 


259.8097 


5371 .5658 


.9 279.2876 


6207.1666 


.fi 240 64()0 


4608.3708 


.8 


260.1239 


5384.5641 


89.0 279.6017 


6221.1389 


.7 ; 240.9602 


4620.4110 


.9 


260.4380 


5397.5782 


.1 279.9159 


6235.1268 


.8 : 241.2743 


4632.4669 


S3.0 


260.7522 


5410.6079 


.2 


280.2301 


6249.1304 


.9 


241.5885 


4614.5384 


.1 


261.0663 


5423.6534 


.3 


280.5442 


6263.1498 


77.0 


241.9026 


4656.6257 


2 


261.3805 


5436.7146 


.4 


280.8584 


6277.1849 


.1 


242.2168 


4668.7287 


'.S 


261.6947 


5449.7915 


F 


281.1725 


6291 2356 


2 


242.5310 


4680.8474 


A 


262.0088 


5462.8840 


!6 


281.4867 


6305.3021 


.3 


242.{y51 


4692.9818 


.5 262.3230 


5475.9923 


.7 


281.8009 


6319.3843 


.4 


243.1593 


4705.1319 


.6 


262.6371 


5489.1163 


.8 


282.1150 


6333.4822 


.5 


243.4734 


4717.2977 


.7 


262.9513 


5502.2561 


.9 


282.4292 


6347.5958 


.6 


243.7876 


4729.4792 


.8 


263.2655 


5515.4115 


90.0 


282.7433 


6361.7251 


.7 


244.1017 


4741.6765 


.9 


263.5796 


5528.5826 


.1 


283.0575 


6375.8701 


.8 


244.4159 


4753.8894 


84.0 


263.8938 


5541.7694 


2 


283.3717 


6390.0309 


.9 


244.7301 


4766.1181 


.1 


264.2079 


5554.9720 


'.i 


283.6858 


6404.2073 


78.0 


245.0442 


4778.3624 


.2 


264.5221 


5568.1902 


A 


284.0000 


6418.3995 


.1 


245.a584 


4790.6225 


.3 


264.8363 


5581.4242 


.5 


284.3141 


6432.6073 


2 


245.6725 


4802.8983 


.4 


265.1504 


£594.6739 


.6 


284.6283 


6446.8309 


!3 


245.9867 


4815.1897 


.5 


265.4646 


5607.9392 


.7 


284.9425 


6461.0701 


.4 


216.3009 


4827.4969 


.6 


265.7787 


5621.2203 


.8 


285.2566 


6475.3251 


.5 


246.6150 


4839.8198 


.7 


266.0929 


5634.5171 


.9 


285.5708 


6489.5958 


.6 


246.9292 


4852.1584 


.8 


266.4071 


5647.8296 


91.0 


285.8849 


6503.8822 


,/ 


:i4T.243? 


4864.5128 


.9 


266.7212 


5661.1578 


.1 


286.1991 


6518.1843 


.8 


M7.5570 


l87b.38?8 


85.0 


26" 0354 


5674.5017 


.2 


286.5133 


6532.5021 


.9 


247.8717 


4889.268& 


.1 


267 3495 


5687.8614 


.3 


286.8274 


6546.8356 


79.0 


248.1858 


4901 .669£ 


.2 


267 6637 


5701.2367 


.4 


287.1416 


6561.1848 


.1 


248.500C' 


4914.0871 


.3 


267 9779 


5714.6277 


.5 


287.4557 


6575.5498 


.2 


248.8141 


4926.5199 


.4 


268.2920 


5728.0345 


.6 


287.7699 


6589.9304 


.3 


249.1283 


4938.9685 


.5 


268.6062 


5741.4569 


.7 


288.0840 


6604.3268 


.4 


249.4425 


4951.4328 


.6 


268.9203 


5754.8951 


.8 


288.3982 


6618.7388 


.5 


249.7566 


4963.9127 


.7 


269.2345 


5768.3490 


.9 


288.7124 


6633.1666 


.6 


250.07 D8 


4976.4084 


.8 


269.5486 


5781.8185 


92.0 


289.0265 


6647.6101 


.7 


250.3843 


4988.n98 


.9 


269.8628 


5795.3038 


.1 


289.3407 


6662.0692 


.8 


250.6991 


50Ci. :469 


86.0 


270.1770 


5808.8048 


.2 


289.6548 


6676.5441 


9 


251.0133 


5013.9897 


.1 


2/0.4911 


5822.3215 


» -'^ 


289.9690 


6691.0347 


80.0 


251.3274 


5026.5482 


2 


270.8053 


5835.8589 


■i 


290.2832 


6705.5410 


.1 


251.6416 


5039.1225 


'.S 


271.1194 


5849.4020 


.5 ! 


290.5973 


6720.0630 


2 


251.9557 


5051.7124 


A 


271.4 3H6 


5862.9659 


.6 


290.9115 


6734.6008 


13 


252.:'699 


5064.3180 


.5 


271.7478 


5876.5454 


.7 


291.2256 


6749.1542 


.4 


252 5840 


5076.9394 


.6 


272.0619 


5890.1407 


.8 


291.5398 


6763.7233 


.5 


252.8982 


5089.5764 


.7 


272.3761 


5903.7516 


.9 


291.8540 


6778.3082 


.6 


253.2124 


5102.2292 


.8 


272.6902 


5917.3783 


93.0 


292.1681 


6792.9087 



ffBCMWPWf 



i i 



From Trautwine's ** Civil Kng-ineer's Pocket Book.*' 



CIRCLES. 



TABLE 2 OF C'IRCIiES— (Continued). 
Diameters in units and tenths. 



Dia. 


Circumf. 


Area. 

6807.5250 


Dia. 

95.5 


Circumf. 


Area. 


Dia. 
97.8 


Circumf. 


Area. 


»«.l 


292.4823 


300.0221 


7163.0276 


307.2478 


7512.2078 


.2 


292.7964 


6822.1569 


.6 


300.3363 


7178.0366 


.9 


307.5619 


7527.5780 


.3 


293.1106 


6836.8046 


.7 


300.6504 


7193.0612 


98.0 


307.8761 


7542.9640 


.4 


293.4248 


6851.4680 


.8 


300.9646 


7208.1016 


.1 


308.1902 


7558.3656 


.5 


293.7389 


6866.1471 


.9 


301.2787 


7223.1577 


.2 


308.5014 


7573.7830 


.6 


294.0.331 


6880.8419 


90.0 


301.5929 


7238.2295 


.3 


308.8186 


7589.2161 


.7 


294.3672 


0895.5524 


.1 


301.9071 


7253.3] 70 


.4 


309.1327 


7604.6648 


.8 


294.6814 


6910.2786 


.2 


302.2212 


7268.4202 


.0 


309.4469 


7620.1293 


.9 


294.99r)6 


6925.0205 


.3 


302.5354 


7283.5391 


.6 


309.7610 


7635.6095 


94.0 ' 295.3097 


6939.7782 


.4 


302.8495 


7298.6737 


.7 


310.0752 


7651.1054 


.1 295.6239 


6954.5515 


.5 


303.1637 


7313.8240 


.8 


310.3894 


7666.6170 


•> 


295.9380 


6969.3406 


.6 


303.4779 


7328.9901 


.9 


310.7035 


7682.1444 


.3 


296.2522 


6984.1453 


.7 


303.7920 


7314.1718 


99.0 


311.0177 


7697.6874 


.4 


296.5663 


6998.9658 


.8 


304.1062 


7359.3693 


.1 


311.3318 


7713.2461 


.5 


296.8805 


7013.8019 


.9 


304.4203 


7374.5824 


.2 


311.6460 


7728.8206 


.6 


297.1947 


7028.6538 


97.0 


304.7S15 


7389.8113 


.3 


311.9602 


7744.4107 


.7 


297.5088 


7043.5214 


.1 


305.0486 


7405.0559 


.4 


312.2743 


7760.0166 


.8 


297.8230 


7058.4047 


.2 


305.3628 


7420.3162 


.0 


312.5885 


7775.6382 


.9 


298.1371 


7073.3037 


.3 


305.6770 


7435.5922 


.6 


312.9026 


7791.2754 


95.0 


298.4513 


7088.2184 


.4 


305.9911 


7450.8839 


.7 


313.2168 


7806.9284 


.1 


298.7655 


7103.1488 


.5 


306.3058 


7466.1913 


.8 


313.5309 


7822.5971 


.2 


299.0796 


7118.0950 


.6 


306.6194 


7481.5144 


.9 


313.8451 


7838.2815 


.3 


299.3938 


7133.0568 


.7- 


306.9336 


7496.8532 


100.0 


314.1593 


7853.9816 


.4 


299.7079 


7148.0343 















Circumferences when the diameter has more than one 
place of decimals. 



Diam. 


Circ. 


Diam. 


Circ. 


1 Diam. 


Circ. 


Diam. 


Circ. 


Diam. 


Circ. 


.1 


.314159 


.01 


.031416 


.001 


.003142 


.0001 


.000314 


.00001 


.000031 


.2 


.628319 


.02 


.062832 


.002 


.006283 


.0002 


.000628 


.00002 


.000063 


.8 


.942478 


.03 


.094248 


.003 


.009425 


.0003 


.000942 


.00003 


.000094 


* 


1.256637 


.04 


.125664 


.004 


.012566 


.0004 


.001257 


.00004 


.000126 


.5 


1 570796 


.05 


.157080 


.005 


.015708 


.0005 


.001571 


.00005 


.000157 


.6 


1.884956 


.06 


.188496 


.006 


.0113850 


.0006 


.001885 


-.00006 


.000188 


.7 


2.199115 


.07 


.219911 


.007 


.021991 


.0007 


.002199 


.00007 


.000220 


.8 


2.513274 


.08 


.251327 


.008 


.025133 


.0008 


.002513 


.00008 


.000251 


.9 


2.827433 


.09 


.282743 


.009 


.028274 


.0009 


.002827 


.00009 


.000283 





Examples. 








Diameter = 3.12699 




Circumfce = 


9.823729 




Circumference == 


S 11 111 of 


Diameter = 




Sum of 


Circ for dia of 3.1 


= 9.738937 


Diii 


for circ of 


9.738937 = 


3,1 


.02 
" .006 
" .0009 
•* .00009 


= .062832 
= .018850 
= .002827 
= .000283 

9.823729 




<i 


.084792 
.062832 = 

.021960 
.018860 = 

.003110 


.02 
.006 








ii 


.002827 = 
.000283 


.0009 








ti 


.000283 = 


.00009 




3.12699 



178 TABLE NO. 73. 

From Tratitwine's *• Civil EngiMeer's Pocket Book." 

CIRCLES. 



TABLE 3 OF CIRCLES. 
Diains in units and twelfths ; as in feet and inches. 



Dia. 


Circumf. 


Area. 


Dia. Circumf. 


Area. 


Dia. 


Circumf. 


Area. 


Ft.In. 


Feet. 


Sq. ft. 


Ft.In. Feet. 


Sq. ft. 


Ft.In. 


Feet. 


Sq. ft. 








5 


15.70796 


19.63495 


10 


31.41593 


78.53982 


1 


.261799 


.005454 


1 


15.96976 


20.29491 


1 


31.67773 


79.85427 


2 


.523599 


.021817 


2 


16.23156 


20.96577 


2 


31.93953 


81.17963 


3 


.785398 


.049087 


3 


16.49336 


21.64754 


3 


32.20132 


82.51589 


4 


1.047198 


.087266 


4 


16.75516 


22.34021 


4 


32.46312 


83.86307 


5 


1.308997 


.136354 


5 


17.01696 


23.04380 


5 


32.72492 


85.22115 


6 


1.570796 


.196350 


6 


17.27876 


23.75829 


6 


32.98672 


86.59015 


7 


1.832596 


.267254 


7 


17.54056 


24.48370 


7 33.24852 


87.97005 


8 


2.094395 


.349066 


8 


17.80236 


25.22001 


8 33.51032 


89.36086 


9 


2.356195 


•441786 


9 


18.06416 


25.96723 


9 33.77212 


90.7625S 


10 


2.617994 


.545415 


10 


18.32596 


26.72535 


10 34.03392 


92.17.520 


11 


2.879793 


.659953 


11 


18.58776 


27.49439 


11 34.29572 


93.-59874 


1 


3.14159 


.785398 


6 


18.84956 


28.27433 


11 34.55752 


95.03318 


1 


3.40339 


.921752 


1 


19.11136 


29.06519 


1 34.81932 


96.47853 


2 


3.66519 


1.06901 


2 


19.37315 


29.86695 


2 35.08112 


97.93479 


3 


3.92699 


1.22718 


3 


19.63495 


30.67962 


3 35.34292 


99.40196 


4 


4.18879 


1.39626 


4 


19.89675 


31.50319 


4 1 35.60472 


100.8800 


5 


4.45059 


1.57625 


5 


20.15855 


32.33768 


5 ! 35.86652 


102.3690 


6 


4.71239 


1.76715 


6 


20.42035 


33.18307 


6 1 36.12832 


103.8689 


7 


4.97419 


1.96895 


7 


20.68215 


34.03937 


7 1 36.39011 


105.3797 


8 


5.23599 


2.18166 


8 


20.94395 


34.90659 


8 1 36.65191 


106.9014 


9 


5,49779 


2.40528 


9 


21.20575 


35.78470 


9 ; 36.91371 


108.4340 


10 


5.75959 


2.63981 


10 


21.46755 


36.67373 


10 


37.17551 


lOy.9776 


11 


6.02139 


2.88525 


11 


21.72935 


37.57367 


11 


37.43731 


111.5320 


9 


6.28319 


3.14159 


7 


21.99115 


38.48451 


12 


37.69911 


113.0973 


1 


6.54498 


3.40885 


1 


22.25295 


39.40626 


1 


37.96U91 


114.6736 


2 


6.80678 


3.68701 


2 


22.51475 


40.33892 


2 


38.22271 


116.2607 


3 


7.06858 


3.97608 


3 


22.77655 


41.28249 


3 


38.48451 


117.85.s8 


4 


7.33038 


4.27606 


4 


23.03835 


42.23697 


4 ] 38.74631 


119.4678 


5 


7.59218 


4.58694 


5 


23.30015 


■43 20235 


5 1 39.00811 


121.0877 


6 


7.85398 


4.90874 


6 


23.56194 


y,..7865 


6 


39,26991 


122.7185 


7 


8.11578 


5.24144 


7 


23.82374 


45.16585 


7 


39.53171 


124.3602 


8 


8.37758 


5.58505 


8 


24.08554 


46.16396 


8 


39.79351 


126.0128 


9 


8.68938 


5.93957 


9 


24.34734 


47.17298 


9 


40.05531 


127.6763 


10 


8.90118 


6.30500 


10 


24.60914 


48.19290 


10 


40.31711 


129.3507 


11 


9.16298 


6.68134 


11 


24.87094 


49.22374 


11 


40.57891 


131.0360 


8 


9.42478 


7.06858 


8 


25.13274 


50.26548 


13 


40.84070 


132.7323 


1 


9.68658 


7.46674 


1 


25.39454 


51.31813 


1 


41.10250 


134.4394 


2 


9.94838 


7.87580 


2 


25.65634 


52.38169 


2 


41.36430 


136.1575 


3 


10.21018 


8.29577 


3 


25.91814 


53.45616 


3 


41.62610 


137.8865 


4 


10.47198 


8.72665 


4 


26.17994 


54.54154 


4 


41.88790 


139.6263 


5 


10.73377 


9.16843 


5 


26.44174 


55.63782 


5 


42.14970 


141.3771 


6 


10.99557 


9.62113 


6 


26.70354 


56.74502 


6 


42.41150 


143.1388 


7 


11.25737 


10.08473 


7 


26.96534 


57.86312 


7 


42.67330 


144.9114 


8 


11.51917 


10.55924 


8 


27.22714 


58.99213 


8 


42.93510 


146.6949 


9 


11.78097 


11.04466 


9 


27.48894 


60.13205 


9 


43.19690 


148.4893 


10 


12.04277 


11.54099 


10 


27.75074 


61.28287 


10 


43.45870 


150.2947 


11 


12.30457 


12.04823 


11 


28.01253 


62.44461 


11 


43.72050 


152.1109 


4 


12.56637 


12.56637 


9 


28.27433 


63.61725 


14 


43.98230 


153.9380 


1 


12.82817 


13.09542 


1 


28.53613 


64.80080 


1 


44.24410 


155.7761 


2 


13.08997 


13.63538 


2 


28.79793 


65.99526 


2 


44.50590 


157.6250 


3 


13.35177 


14.18625 


3 


29.05973 


67.20063 


3 


44.76770 


159.484G 


4 


13.61357 


14.74803 


4 


29.32153 


68.41691 


4 


45.02949 


161.3557 


5 


13.87537 


15.32072 


5 


29.58333 


69.64409 


5 


45.29129 


163.2374 


6 


14.13717 


15.90431 


6 


29.84513 


70.88218 


6 


45.55309 


165.1300 


7 


14.39897 


16.49882 


7 


30.10693 


72.13119 


7 


45.81489 


167.033.5 


8 


14.66077 


17.10423 


8 


30.36873 


73.39110 


8 


46.07669 


168.9478 


9 


14.92257 


17.72055 


9 


30.63053 


74.66191 


9 


46.33849 


170.8732 


10 


15,18436 


18.34777 


10 


30.89233 


75.94364 


10 


46.60029 


172.8094 


11 


15.44616 


18.98591 


11 


31.15413 


77.23627 


11 


46.86209 


174.7565 



From Traut^'ine's ''Ci^'il Eng^ineer's Pocket Book." 



CIRCLES. 



TABL.E 3 OF CIRCLES— (Continued). 
Diams in units and twelfths; as in feet and inclies. 



Dia. 


Circunif. 


Area. 


Dia. 


Circanif. 


Area. 


Dia. 


Circunif. 


Area. 


Ft.In. 


Feet. 


Sq. ft. 


Ft.In. 


Feet. 


Sq. ft. 


Ft.In. 


Feet. 


Sq. ft. 


15 


47.12389 


176.7146 


20 


62.83185 


314.1593 


25 


78.53982 


490.8739 


1 


47.38569 


178.6835 


1 


63.09365 


316.7827 


1 


78.80162 


494.1518 


2 


47.64749 


180.6634 


2 


63.35545 


319.4171 


2 


79.06842 


497.4407 


3 


47.90929 


182.6542 


3 


63.61725 


322.0623 


3 


79.32521 


500.7404 


4 


48.17109 


184.6558 


4 


63.87905 


324.7185 


4 i 79.58701 


504.0511 


5 


48.43289 


186.6684 


5 


64.11085 


327.3856 


5 i 79.84881 


507.3727 


6 


48.69469 


188.6919 


6 


64.40265 


330.0636 


6 [ 80.11061 


510.7052 


7 


48.95649 


190.7263 


/ 


64.66445 


332.7525 


7 i 80.37241 


514.0486 


8 


49.21828 


192.7716 


8 


64.92625 


335.4523 


8 ! 80.63421 


517.4029 


9 


49.48008 


194.8278 


9 


65.18805 


338.1680 


9 80.89601 


520.7681 


10 


49.74188 


1 96-. 8950 


10 


65.44985 


340.8846 


10 • 81.15781 


524.1442 


11 


50.00368 


198-9780 


11 


65.71165 


343.6172 


11 81.41961 


527.5312 


16 


50.2G548 


201.0619 


21 


65.97345 


346.3606 


26 81.68141 


530.9292 


1 


50.52728 


203.1618 


1 


66.23525 


349.1149 


1 81.94321 


534.3380 


2 


50.78908 


205.2725 


2 


66.49704 


351.8»02 


2 ! 82.20501 


537.7578 


3 


51.05088 


207.3942 


3 


66.75884 


a54.6564 


3 82.46681 


541.1884 


4 


51.31268 


209.5268 


4 


67.02064 


357.4484 


4 : 82.72861 


544.6300 


5 


51.57448 


211.6703 


5 


67.28244 


360.2414 


5 82.99041 


548.0825 


6 


51.836-J8 


213.8246 


6 


67.54424 


363.0508 


6 83.25221 


551.5459 


7 


52.09808 


215.9899 


7 


67.80604 


365.8701 


7 1 83.51400 


555.0202 


8 


52.a5988 


218.1662 


8 


68.06784 


368.7008 


8 83.77580 


558.5054 


9 


52.62168 


220.3533 


9 


68.32964 


371.5424 


9 84.03760 


562.0015 


10 


52.88348 


222.5513 


10 


68.59144 


374.3949 


10 1 84.29940 


565.5085 


11 


53.14528 


224.7602 


11 


68.85324 


377.2584 


11 84.56120 


569.0264 


17 


53.40708 


226.9801 


22 


69.11504 


380.1327 


27 84.82300 


572.5553 


1 


53.66887 


229.2108 


1 


69 37684 


383.0180 


1 85.08480 


576.0950 


2 


53.93067 


231.4.525 


') 


69.63864 


385.9141 


2 &5.34660 


579.6457 


3 


54.19247 


233.7050 


3 


69.90044 


388.8212 


3 85.60840 


583.2072 


4 


54.45427 


235.968.5 


4 


70.16224 


391.7392 


4 8.5.87020 


586.7797 


5 


.54.71607 


238.2429 


5 


70.42404 


394.6680 


5 i 86.13200 


590.3631 


6 


54.97787 


240.5282 


6 


70.68583 


397.6078 


6 ; 86.39380 


593.9574 


7 


5.5.23967 


242.8244 


7 


70.94763 


400.5585 


7 ' 86.65560 


597.5626 


8 


55.50147 


245.1315 


8 


71.20943 


403.5'201 


8 86.91740 


601.1787 


9 


55.76327 


247.4495 


9 


71.47123 


406.4926 


9 87.17920 


604.8057 


10 


56.02507 


249.7784 


10 


71.73303 


409.4761 


10 87.44100 


608.4436 


11 


.56.28687 


252.1183 


11 


71.99488 


412.4704 


11 87.70279 


612.0924 


18 


.56.54867 


2.54.4690 


23 


72.25663 


415.4756 


28 87.96459 


615.7522 


1 


56.81047 


256.8307 


1 


72.51843 


418.4918 


1 88.22639 


619.4228 


2 


57.07227 


259.2032 


2 


72.78023 


421.5188 


2 88.48819 


623.1044 


3 


57.33407 


261.5867 


3 


73.04208 


424.5.568 


3 88.74999 


626.7968 


4 


57.59587 


263.9810 


4 


73.30383 


427.6057 


4 89.01179 


630.5002 


5 


57.85766 


266.3863 


5 


73.56568 


430 6654 


5 89.27359 


634.2145 


6 


58.11946 


268.8025 


6 


73.82743 


433.7361 


6 89.53539 


637.9397 


7 


58.38126 


271.2296 


7 


74.08923 


436.8177 


7 89.79719 


641.6758 


8 


58.64306 


273.6676 


8 


74.35103 


439.9102 


8 90.05899 


645.4228 


9 


58.90486 


276.1165 


9 


74.61283 


443.0137 


9 90.82079 


649.1807 


10 


59.16666 


278.5764 


10 


74.87462 


446.1280 


10 90.58259 


652.9495 


11 


.59.42846 


281.0471 


11 


75.13642 


449.2532 


11 90.84489 


656.7292 


19 


59.69026 


283.5287 


24 


75.39822 


4.52.8893 


29 91.10619 


660.5199 


1 


59.95206 


286.0213 


1 


75.66002 


455..5364 


1 91.36799 


664.3214 


2 


60.21386 


288.5247 


2 


75.92182 


458.6943 


2 : 91.62979 


668.1339 


3 


60.47566 


291.0391 


3 


76.18362 


461.8632 


3 ■ 91.89159 


671.9572 


4 


60.73746 


293.5644 


4 


76.44.542 


465.0480 


4 92.15338 


675.791a 


5 


60.99926 


296.1006 


5 


76.70722 


468.2337 


5 92.41518 


679.6367 


6 


61.26106 


298.6477 


6 


76.96902 


471.4852 


6 92.67698 


683.492? 


7 


61.52286 


301.2056 


7 


77.23082 


474.6477 


7 


92.93878 


687.3591 


8 


61.78466 


303.7746 


8 


77.49262 


477.871 1 


8 


93.20058 


691.237'! 


9 ! 62.04645 


306.3.544 


9 


77.75442 


481.1055 


9 


93.46238 


695.1263 


10 


62.30825 


.308.9151 


10 


78.01622 


484.3507 


10 


93.72418 


699.026: 
702.936) 


11 


62.57005 


311. .5467 


11 


78.27802 


487.6068 


11 


93.98598 



180 TABLE NO. 73-CON. 

From Trautwine's "Civil Engineer's Pocket Book.' 

CIRCLES. 



TABIiE 3 OF CIRCIiES— (Continued). 
Diams in units and twelfths; as in feet and inches. 



Dia. jcircamf. 


Area. 


Dia. 


Circumf. 


Area. 


Dia. 


Circumf. 


Area. 

! 


Ft. In. 


Feet. 


Sq. ft. 


Ft.In 


Feet. 


Sq. ft. 


Ft.In. 


Feet. 


Sq. ft. 


30 


94.24778 


706.8583 


35 


109.9557 


962.1128 


40 


125.6637 


1256.6371 


1 


94.50958 


710.7908 


1 


110.2175 


966.6997 


1 


125.9255 1 1261.8785 


2 


94.77138 


714.7341 


2 


110.4793 


971.2975 


2 


126.1873 1 1267.1309 


3 


95.03318 


718.6884 


3 


110.7411 


975.9063 


3 


126.4491 


1272.3941 


4 


95.2SJ498 


722.6536 


4 


111.0029 


980.5260 


4 


126.7109 


1277.6683 


5 


95.55678 


726.6297 


5 


111.2647 


985.1566 


5 


126.9727 


1282.9534 


6 


95.81858 


730.6166 


6 


111.5265 


989.7980 


6 


127.2345 


1288.2493 


7 


96.08038 


734.6145 


7 


111.7883 


994.4504 


7 


127.4963 


1293.5562 


8 


96.34217 


738.6233 


8 


112.0501 


999.1137 


8 


127.7561 


1298.8740 


9 


96.60397 


742.6431 


9 


112.3119 


1003.7879 


9 


128.0199 


1304.2027 


10 


96.86577 


746 6737 


10 


112.5737 


1008.4731 


10 


128.2817 


1309.5424 


11 


97.12757 


750.7152 


11 


112.8355 


1013.1G91 


11 


128.5435 


1314.8929 


31 


97.38937 


754.7676 


36 


113.0973 


1017.8760 


41 


128.8053 


1320.2543 


1 


97.65117 


758.8310 


1 


113.3591 


1022.5939 


1 


129.0671 


1325.6267 


2 


97.91297 


762.9052 


2 


113.6209 


1027.3226 


2 


129.3289 


1331.0099 


3 


98.17477 


766.9904 


3 


113.8827 


1032.0623 


3 


129.5907 


1336.4041 


4 


98.43657 


771.0865 


4 


114.1445 


1036.8128 


4 


129.8525 


1341.8091 


5 


98.69837 


775.1934 


5 


114.4063 


1041.5743 


5 


130.1143 


1347.2251 


6 


98.96017 


779.3113 


6 


114.6681 


1046.3467 


6 


130.3761 


1352.6520 


7 


99.22197 


783.4401 


7 


114.9299 


1051.1300 


7 


130.6379 


1358.0898 


8 


99.48377 


787.5798 


8 


115.1917 


1055.9242 


8 


130.8997 


1363.5385 


9 


99.74557 


791.7304 


9 


115.4535 


1060.7293 


9 


131.1615 


1368.9981 


10 


100.0074 


V95.8920 


10 


115.7153 


1065.5453 


10 


131.4233 


1374.4686 


11 


100.2692 


800.0644 


11 


115.9771 


1070.3723 


11 


131.6851 


1379.9500 


32 


100.5310 


804.2477 


3? 


116.2389 


1075.2101 


42 


131.9469 


1385.4424 


1 


100.7928 


808.4420 


1 


116.5007 


1080.0588 


1 


132.2087 


1390.9456 


2 


101.0546 


812.6471 


2 


116.7625 


1084.9185 


2 


132.4705 


1396.4598 


3 


101.3164 


816.8632 


3 


117.0243 


1089.78C0 


3 


132.7323 


1401.9848 


4 


101.5782 


821.0901 


4 


117.2861 


1094.6705 


4 


132.9941 


1407.5208 


5 


101.8400 


825.3280 


5 


117.5479 


1099.5629 


5 


133.2559 


1413.0676 


6 


102.1018 


829 5768 


6 


117.8097 


1104.4662 


6 


133.5177 


1418.6254 


7 


102.3636 


833.8365 


7 


118.0715 


1109.3804 


7 


133.7795 


1424.1941 


8 


102.6254 


838.1071 


8 


118.3333 


1114.3055 


8 


134.0413 


1429.7737 


9 


102.8872 


842.3886 


9 


118.5951 


1119.2415 


9 


134.3031 


1435.3642 


10 


103.1490 


846.6810 


10 


J 18.8509 


1124.1884 


10 


134.5649 


1440.9656 


11 


103.4108 


850.9844 


11 


119.1187 


1129.1462 


11 


134.8267 


1446.5780 


33 


103.6726 


855.2986 


38 


119.3805 


1134.1149 


43 


135.0885 


1452.2012 


1 


103.9344 


8.59.6237 


1 


119.6423 


1139.0946 


1 


135.3503 


1457.8353 


2 


104.1962 


863.9598 


2 


1,9.9041 


1144.0851 


2 


135.6121 


1463.4804 


3 


104.4580 


868.3068 


3 


120.1659 


1149.0866 


3 


135.8739 


1469.1364 


4 


104.7198 


872.6646 


4 


120.4277 


1154.0990 


4 


136.1357 


1474.8032 


5 


104.9816 


877.0334 


5 


120.6895 


1159.1222 


5 


136.3975 


1480.4810 


6 


105.2434 


881.4131 


G 


120.9513 


1164.1564 


6 


136.6593 


1486.1697 


7 


105.5052 


885.8037 


7 


121.213J 


1169.2015 


7 


136.9211 


1491.8693 


8 


105.7670 


890.2052 


8 


121.4749 


1174.2575 


8 


137.1829 


1497.5798 


9 


106.0288 


894.6176 


9 


121.7367 


1179.3244 


9 


137.4447 


1503.3012 


10 


106.290(5 


899 0409 


10 


121.9985 


1184.4022 


10 


137.7065 


1509.0335 


. 11 


106.5524 


903.4751 


11 


122.2603 


1189.4910 


11 


137.9683 


1514.7767 


34 


106.8142 


907.9203 


39 


122.5221 


1194.5906 


44 


138.2301 


1520.5308 


1 


107.0759 


9J 2.3763 


1 


122.7839 


1199.7011 


1 


138.4919 


1526.2959 


2 


107.3377 


916.8433 


2 


123.0457 


1204.8226 


2 


138.7537 


1532.0718 


3 


107.5995 


921.3211 


3 


123.3075 


1209.9550 


3 


139.0155 


1537.8587 


4 


107.8613 


925.8099 


4 


123.5693 


1215.0982 


4 


139.2773 


1543.6565 


5 


108.1231 


930.3096 


5 


123.8311 


1220.2524 


5 


139.5391 


1549.4651 


5i 


108.3849 


934.8202 


6 


124.0929 


1225.4175 


6 


139.8009 


1555.2847 


7 


108.6467 


939.3417 


7 


124.3547 


1230.5935 


7 


140.0627 


1561.1152 


8 


108.9085 


943.8741 


8 


124.6165 


1235.7804 


8 


140.3245 


1566.9566 


9 


109.1703 


948.4174 


9 


124.8783 


1240.9782 


9 


140.5863 


1572.8089 


10 


109.4321 


952.9716 


10 


125.1401 


1246.1869 


10 


140.8481 


1578.6721 


. 11 


109.6939 


957.5367 


11 i 


125.4019 


1251.4065 


11 141.1099 


1584.5462 



TABLE NO. 73— CON. 181 

From Trautwine's "civii jc<ti^Aiieer'!» l*ocket Book." 

CIRCLES. 



TABIiE 3 OF CIRCLES— (Continued). 
l>iains in units and twelfths; as in feet and inches. 



Dia. 


C'ircumf. Area. 


Dia. Circumf. Area. 


Dia. 


C'ircumf. 


1 

Area. 


Ft.In 


Feet. 


Sq. ft. 


Ft.Iu.' Feet. Sq. ft. 


Ft.lQ 


Feet. 


Sq. ft. 


4a 


141.3717 


1590.4313 


50 ! 157.0796 ' 1963.4954 


55 


172.7876 i 2375.8294 


1 i 141.6335 


1596.3272 


1 : 157.3414 1970.0458 


1 


173.0494 1 2383.0344 


2 


141.8953 


1602.2341 


2 157.6032 1976.6072 


2 


173.3112 2390.2502 


3 


142.1571 


1608.1518 


3 157.8650 ! 1983.1794 


3 


173.5730 2397.4770 


4 


142.4189 


1614.0805 


4 


158.1268 i 1989.7626 


4 


173.8348 


; 2404.7146 


5 


142.6807 


1620.0201 


5 


158.3886 1996 3567 


5 


174.0966 


2411.9632 


6 


142.9425 i 1625.9705 


6 


158.6504 2UU2.9617 


6 


174.3584 


2419.2227 


7 


143.2043 t 1631.9319 


7 


158.9122 : 2009.5776 


7 


174.6202 


2426.4931 


8 


143.4661 I 1637.9042 


8 


159.1740 ; 2016.2044 


8 


174.8820 


2433.7744 


9 


143.7279 i 1643.8874 


9 


159.4358 1 2022.8421 


9 


175.1438 


2441.0666 


10 


143.9897 ; 1649.8816 


10 


, 159.6976 2029.4907 


10 


175.4056 


2448.3697 


11 j 144.2515 1655.8.S86 


11 


159.9594 1 2036.1502 


11 


175.6674 


' 2455.6837 


46 ■ 144.5138 1661.9025 


51 


' 160.2212 : 2042.8206 


56 


175.9292 


2463.0086 


1 144.7751 1667.9294 


1 


160.4830 : 2049.5020 


1 


176.1910 


2470.3445 


2 145.0369 1673.9671 


2 


' 160.7448 ! 2056.1942 


2 


176.4528 


2477.6912 


3 145.2987 1680.0158 


3 


: 161.0066 


1 2062.8974 


3 


176.7146 


248.5.0489 


4 145.5605 


1686.0753 


4 


' 161.2684 


2069.6114 


4 


176.9764 


2492.4174 


5 145.8228 


1692.1458 


5 


1 161.5302 


! 2076.3364 


5 


177.2382 


2499.7969 


6 146.0841 


1698.2272 


6 


161.7920 


i 2083.0723 


6 


177.5000 


2507.1873 


7 146.3459 


1704.3195 


7 


162.0538 


2089.8191 


7 


177.7618 


2514.5886 


8 546.6077 


1710.4227 


8 


162.3156 


[ 2096.5768 


8 


178.0236 


2522.0008 


9 146.8695 


1716.5368 


9 


162.5774 


I 2103.3454 


9 


178.2854 


2529.4239 


10 147.1313 


1722.6618 


10 


162.8392 


' 2110.1249 


10 


178.5472 


2536.8579 


11 


147.3931 


1728.7977 


11 


163.1010 


2116.9153 


11 


178.8090 


2544.3028 


47 


147.6549 


1734.9445 


.52 


163.3628 


2123.7166 


57 


179.0708 


2551.7586 


1 


147.9167 


1741.1023 


1 


163.6246 


2130.5289 


1 


179.3326 


2559.2254 


2 


148.1785 


1747.2709 


2 


163.8864 


2137.3520 


2 


179.5944 


2566.7030 


3 


148.4403 


1753.4505 


3 


164.1482 


2144.1861 


3 


179.8562 


2574.1916 


4 


148.7021 


1759.6410 


4 


164.4100 


2151.0310 


4 


180.1180 , 2581.6910 


5 


148.9639 


1765.8423 


5 


164.6718 


2157.8869 


5 


180.379-.- 


2589.2014 


6 


149.2257 


1772.0546 


6 


164.9336 


2164.7537 


6 


180.6416 


25^6.7227 


7 


149.4875 


1778.2778 


7 


165.19,54 


2171.6314 


7 


180.9034 


2604.2549 


8 


149.7492 


1784.5119 


8 


165.4572 


2178.5200 


8 


181.1652 


2611.79S0 


9 


150.0110 


1790.7569 


9 


165.7190 


2185.4195 


9 


181.4270 


2619.3520 


10 


150.2728 


1797.0128 


10 


165.9808 


2192.3299 


10 


181.6888 


2626.9169 


11 


150.5346 


1803.2796 


11 


166.2426 


2199.2512 


11 


181.9506 


2634.4927 


48 


150.7964 


1809.5574 


53 


166.5044 


2206.1834 


58 


182.2124 


2642.0794 


1 


151.0582 


1815.8460 


1 


166.7662 


2213.1266 


1 


182.4742 


2649.6771 


2 


151.3200 


1822 1456 


2 


167.0280 


2220.0806 


2 


182.7360 


2657.2856 


3 


151.5818 


1828.456U 


3 


167.2898 


2227.0456 


3 


182.9978 , 


2664.9051 


4 


151.8436 


1834.7774 


4 


167.5516 


2234.0214 


4 


183.2596 I 


2672.5354 


5 


152.1054 


1841.1096 


5 


167.8134 


2241.0082 


5 


183.5214 1 


2680.1767 


6 


152.3672 


1847.4528 


6 


168.0752 


2248.0059 


6 


183.7832 


2687.8289 


7 


152.6290 ' 1853.8069 


7 


168.3370 


2255.0145 


7 


184.0450 2695.4920 


8 


152.8908 1860.1719 


8 


168.5988 2262.0340 


8 


184.3068 2703.1659 


9 


153.1526 1866.5478 


9 


168.8606 2269.0644 


9 


184.5686 2710.8508 


10 153.4144 


1872.9346 


10 


169.1224 2276.1057 


10 


184.8304 2718.5467 


11 


153.6762 


1879.3324 


11 


169.3842 2283.1579 


11 


185.0922 2726.25:34 


49 


153.9380 


1885.7410 


.54 


169.6460 2290.2210 


59 


185.3540 


2733.9710 


1 


154.1998 


1892.1605 


1 


169.9078 2297.2951 


1 


185.6158 


2741.6995 


2 ' 154.4616 


1898.5910 


2 


170.1696 2304.3800 


2 i 


185.8776 


2719.4390 


3 


154.7234 


1905.0323 


3 


170.4314 2311.4759 


3 


186.1394 


2757.1893 


41 


154.9852 


1911.4846 


4 


170.6932 


2318.5826 


4 


186.4012 ! 


2764.9506 


5 


155 2470 


1917.9478 


5 


170.9550 


2325.7003 


5 


186.6630 


2772.7228 


6 


155.5088 


1924.4218 


6 


171.2168 


2332.8289 


6 


186.9248 


2780.5058 


7 


155.7706 ! 


1930.9068 


7 


171.4786 


2339.9684 


7 


187.1866 


2788.2998 


8 


156.0324 1 


1937.4027 


8 


171.7404 


2347.1188 


8 


187.4484 


2796.1047 


9 


156.2942 ! 


1943.9095 


9 


172.0022 


23.54.2801 


9 


187.7102 


2803.9205 


10 


156.5560 ' 


1950.4273 


10 


172.2W0 


2361.4523 


10 


187.9720 


2811.7472 


11 

1 


156.8178 


1956.9559 


11 


172.5258 


2368.6354 


11 


188.2338 


2819.584& 



wmmmmmm 



From Trautwine's "Civil Engineer's PocUet Book.** 



CIRCLES. 



TABL.£ 3 OF CIRCI.ES— (Continued). 
Diams in units and twelfths; as in feet and inches. 



Dia. 


Circumf. 


Area. 


Dia. 


Circumf. 


Area. 


Dia. 


Circumf. 


Area. 


Ft.In. 


Feet. 


Sq. ft. 


Ft.Iu, 


Feet. 


Sq. ft. 


Ft.In. 


Feet. 


Sq. ft. 


60 


188.4956 


2827.4334 


65 


204.2035 


3318.3072 


70 


219.9115 


3848.4510 


1 


188.7574 


2835.2928 


1 


204.4653 


3326.8212 


1 


220.1733 


3857.6194 


2 


189.0192 


2843.1632 


2 


204.7271 


3335.;^60 


2 


220.4351 


3866.7988 


3 


189.2810 


2851.0444 


3 


204.9889 


3343.8818 


3 


220.6969 


387-5.9890 


4 


189.5428 


2858.9366 


4 


205.2507 


3352.4284 


4 


220.9587 


3885.1902 


5 


189.8046 


2866.8397 


5 


205.5125 


3360.9860 


5 


221.2205 


3894.4022 


6 


190.0664 


2874.7536 


6 


205.7743 


3369.5546 


6 


221.4823 


3903.6252 


7 


190.3282 


2882.6785 


7 


206.0361 


3378.1339 


7 


221.7441 


3912.8591 


8 


190.5900 


2890.6143 


8 


206.2979 


3386.7241 


8 


222.0059 


3922.1039 


9 


190.8518 


2898.5610 


9 


206.5597 


3395.3253 


9 


222.2677 


3931.3596 


10 


191.1136 


2906.5186 


10 


206.8215 


3403.9375 


10 


222.5295 


3940.6262 


11 


191.3754 


2914.4871 


11 


207.0833 


3412.5605 


11 ! 222.7913 


3949.9037 


61 


191.6372 


2922.4666 


66 


207.3451 


3421.1944 


71 ; 223.0531 


3959.1921 


1 


191.8990 


2930.4569 


1 


207.6069 


3429.8392 


1 1 223.3149 


3968.4915 


2 


192.1608 


2938.4581 


2 


207.8687 


3438.4950 


2 


223.5767 


3977.8017 


3 


192.4226 


2946.4703 


3 


208.1305 


3447.1616 


3 


223.8385 


3987.1229 


4 


192.6843 


2954.4934 


4 


208.3923 


3455.8392 


4 


224.1003 


3996.4549 


5 


192.9461 


2962.5273 


5 


208.6541 


3464.5277 


5 


224.3621 


4005.7979 


6 


193.2079 


2970.5722 


6 


208.9159 


3473.2270 


6 1 224.6239 


4015.1518 


7 


193.4697 


2978.6280 


7 


209.1777 


3481.9373 


7 ! 224.8857 


4024 5165 


8 


193.7315 


2986.6947 


8 


209.4395 


3490.6585 


8 1 225.1475 


4033.8922 


9 


193.9933 


2994.7723 


9 


209.7013 


3499.3906 


9 1 225.4093 


4043.2788 


10 


194.2551 


3002.8608 


10 


209.9631 


3508.1336 


10 i 225.6711 


4052.6763 


11 


194.5169 


3010.9602 


11 


210.2249 


3516.8875 


11 1 225.9329 


4062.0848 


62 


194.7787 


3019.0705 


67 


210.4867 


3525.6524 


72 ; 226.1947 


4071.5041 


1 


195.0405 


3027.1918 


1 


210.7485 


3534.4281 


1 


226.4565 


4080.9343 


2 


195.3023 


3035.3239 


2 


211.0103 


3543.2147 


2 


226.7183 


4090.3755 


8 


195.5641 


3043.4670 


3 


211.2721 


3552.0123 


3 


226.9801 


4099.8275 


4 


195.8259 


3051.6209 


4 


211.5339 


3560.8207 


4 


227.2419 


4109.2905 


5 


196.0877 


3059.7858 


5 


211.7957 


3569.6401 


5 


227.5037 


4118.7643 


6 


196.3495 


3067.9616 


6 


212.0575 


3578.4704 


6 


227.76.55 


4128.2491 


7 


196.6113 


3076.1483 


7 


212.3193 


3587.3116 


7 


228.0273 


4137.7448 


8 


196.8731 


3084.3459 


8 


212.5811 


3596.1637 


8 : 228.2891 


4147.2514 


9 


197.1349 


8092.5544 


9 


212.8429 


3605.0267 


9 


228.5509 


4156.7689 


10 


197.3967 


3100.7738 


10 


213.1047 


3613.9006 


10 


228.8127 


4166.2973 


n 


19T.6585 


3109.0041 


11 


213.3665 


3622.7854 


11 


229.0745 


4175.8366 


63 


197.9203 


3117.2453 


68 


213.6283 


3631.6811 


73 


229.3363 


4185.8868 


1 


198.1821 


3125.4974 


1 


213.8901 


3640.5877 


1 


229.5981 


4194.9479 


2 


198.4439 


3133.7605 


2 


214.1519 


3649.5053 


2 


229 8599 


4204.5200 


3 


198.7057 


3142.0344 


3 


214.4137 


3G58.4337 


3 


280.1217 


4214.1029 


4 198.9675 


3150.3193 


4 


214.67.55 


3667.3731 


4 


230.3835 


4223.6968 


5 


199.2293 


3158.6151 


5 


214.9373 


3676.3234 


5 


230.6453 


4233.3016 


6 


199.4911 


3166.9217 


6 


215.1991 


3685.2845 


6 


230.9071 


4242.9172 


7 


199.7529 


3175.2393 


7 


215.4609 


3694.2566 


7 


231.1689 


4252.5438 


8 


200.0147 


3183.5678 


8 


215.7227 


3703.2396 


8 


231.4307 


4262.1813 


9 


200.2765 


3191.9072 


9 


215.9845 


3712.2335 


9 


231.6925 


4271.8297 


10 


200.5383 


3200.2570 


10 


216.2463 


3721.2383 


10 


231.9543 


4281.4890 


11 


200.8001 


3208.6188 


11 216.5081 


3730.2540 


11 


232.2161 


4291.1592 


64 


201.0619 


3216.9909 


69 . 216.7699 


3739.2807 


74 


232.4779 


4300.8403 


1 


201.3237 


3225.3739 


1 i 217.0317 


3748.3182 


1 


232.7397 


4310.5324 


2 


201.5855 


3233.7679 


2 ■ 217.2935 


3757.3666 


2^ 


233.0015 


4320.2353 


3 


201.8473 


3242.1727 


3 i 217.5553 


3766.4260 


3 


233.2633 


4329.9492 


4 


202.1091 


3250.5885 


4 i 217.8171 


3775 4962 


4 


233.5251 


4339.6739 


5 


202.3709 


3259.0151 


5 1 218.0789 


3784.5774 


5 


233.7869 


4349.4096 


6 


202.6327 


3267.4527 


6 i 218.3407 


3793.6695 


6 


234.0487 


4359.1562 


7 


202.8945 


3275.9012 


7 ' 218.6025 


3802.7725 


7 


234.3105 


4368.9136 


8 


203.1563 


3284.3606 


8 ! 218.8643 


3811.8864 


8 


234.5723 


4378.6820 


9 


203.4181 


3292.8309 


9 219.1261 


3821.0112 


9 


234.8341 


4388.4613 


10 


203.6799 


3301.3121 


10 


219.3879 


3830.1469 


10 


2.35.0959 


4398.2515 


11 


203.9417 


3309.8042 


11 


219.6497 


3839.2935 


11 


235.3576 


4408.0526 



TABLE NO. 73— CON. 183 

From Trantwiiie's •* Civil Engineer's Pocket Book." 

CIRCLES. 



TABIiK 3 OF CIRCL.es— (Continued;. 
]>ianis in units and twelfths; as in feet anti inches. 



Dia. 


Circumf. 


Area. 


Dia. 


Circuinf. Area. 


Dia. Circumf. Area. 


Ft.Iu. 


Jj'uel. 


S(i. ft. 


Ft.In. 


Feet. 


Sq. ft. 


Ft.In. 


Feet, j Sq. ft. 


75 


235.6194 


4417.8647 


80 


251.3274 


5026.5482 


So 


267.03-54 5674.-r.Ol7 


1 


235.8812 


4427.6676 


1 


251.5892 


5037.0257 


1 


267.2972 5685 6337 


2 


236.1430 


4437.5214 


2 


251.8510 


5047.5140 


2 


267..3.:90 


5696.7763 


3 


236.4048 


4447.3(362 


3 


252.1128 


5058.0133 


3 


267.8208 


5707.9302 


4 


236.6666 


4457.2218 


4 


252.3746 


5068.5234 


4 


268 0826 


5719.uy>9 


5 


236.9284 


4467.0884 


5 


252.6364 


5079.0445 


5 


268 3444 


5730.27IJ5 


6 


237.1902 


4476.9659 


6 


252.8982 


5089.5764 


6 


268.6062 


5741.4-369 


7 


237.4520 


4483.8543 


7 


253.1600 


5100.1193 


7 


268.8b80 


5752.6543 


8 


237.7138 


4496.7536 


8 


253.4218 


5110.6731 


8 


269.1298 


5763.861:6 


9 


237.9756 


4506.6637 


9 


253.6836 


5121.2378 


9 


269.3916 


5775.0bl« 


10 


238.2374 


4516.5849 


10 


233.9454 


5131.8134 


10 


269.6534 


5786.3119 


11 


238.4992 


4526.5169 


11 


254.2072 


5142.3999 


11 


269.91.'2 


5797.5329 


76 


238.7610 


4536.4598 


81 


254.4690 


5152.9974 


S6 


270.1770 


.'808 s048 


1 


239.0228 


4546.4136 


1 


254.7308 


5163.6057 


1 


270.4388 


5820.0676 


2 


239.2846 


4556.3784 


2 


254.9926 


5174.2249 


2 


270.7006 


5831:5414 


3 


239.5464 


4566.3510 


3 


255.2544 


5184.8-35] 


3 


270.9624 


5842.62ti0 


4 


239.8082 


4576.3406 


4 


255.5162 


5195.4961 


4 


271 2242 


5853.9216 


5 


240.0700 


4586.3380 


5 


2.35.7780 


5206.145.1 


5 


271.4860 


5865.2280 


6 


240.3318 


4596.3464 


6 


256.0398 


5216.8110 


6 


271.7478 


5876.54.34 


7 


240.5936 


4606.3657 


7 


256.3016 


5227.4847 


7 


272.0096 


5887.8737 


8 


240.8554 


4616.3959 


8 


256.5631 


5238.1694 


8 


272.2714 


5899.2120 


9 


241.1172 


4626.4370 


9 


256.8252 


5248.8650 


9 


272.5332 


5910..r,630 


10 


241.3790 


4636.4890 


10 


257.0870 


52.395715 


10 


272.79.30 5921 L-240 


11 


241.6408 


4646.5519 


11 


257.3488 | 5270.2889 


11 


273.0568 5933 •_y59 


77 


241.9026 


46.36.62.37 


82 


257.6106 5281.0173 


87 


273 3186 5944 1. 7 .S7 


1 


242.1644 


4666.7104 


1 


257.8724 I 5291.7565 


1 


273..".804 5956.0724 


2 


242.4262 


4676.8061 


2 


238.1342 


5302.5066 


2 


273.8422 5967.4771 


3 


242.6880 


4686.9126 


3 


258.396U 


5313.2677 


3 


274.1040 


5978.8926 


4 


242.9498 


4697.0301 


4 


258.6578 


5324.0396 


4 


274.3658 


5990.3191 


5 


243.2116 


4707.1584 


5 


258.9196 


5334.8225 


5 


274.6276 


6001.7.364 


6 


243.4734 


4717.2977 


6 


259.1814 


5345.6162 


6 


274.8894 


6013.2047 


7 


213.7352 


4727.4479 


7 


259.4432 


5356.4209 


7 


275.1512 6024.6631^ 


8 


243.9970 


4737.6090 


8 


2.39.7050 


5367.2365 


8 


275.4130 


6036.1341 


9 


244.2588 


4747.7810 


9 


2.39.9668 


5.378.0630 


9 


275.6748 


6047.6149 


10 


244.5206 


4757.9639 


10 


260.2286 


5388 9004 


10 


275.9366 


6059.1065 


11 


244.7824 


4768.1577 


11 


260.4904 


5399.7487 


11 


276.1 9S4 


6070.6097 


78 


245.0442 


4778.3624 


83 


260.7.322 i 5410.6079 


88 


276.4602 


6082.1234 


1 


245.3060 


4788.5781 


1 


261.0140 


5421.4781 


1 


276.7220 


6093.64 8<J 


2 


215.5678 


4798.8046 


2 


261.2758 


5432.3591 


2 


276.9838 6105.1835 


8 


245.8296 


4809.0420 


3 


261.5376 


5443.2-311 


3 


277.24.36 6116.7300 


4 


246.0914 


4819.2904 


4 


261.7994 ! 54-34.1539 


4 


277.-3074 6128.2^73 


5 


246.a532 


4829.-3497 


5 


262.0612 ! 5465.0677 


5 


277.7692 6139.8-'.-36 


6 


246.6150 


4839.8198 


6 


262.3230 


5475.9923 


6 


278.0309 6151. 434S 


7 ; 246.8768 


4850.1009 


7 


262.5848 


5486.9279 


7 


278.2927 6163.0.48 


8 247.1386 


4860.3929 


8 


262.8166 


5497.8744 


8 


278.5545 6174.6258 


9 247.4004 


4870 6958 


9 


263.1084 


5508.8318 


9 


278.8163 6186.2377 


10 247.6622 


4881.0096 


10 


263.3702 


5519.8001 


10 


279.0781 6197.b605 


11 247.9240 


4891.3343 


11 


263.6320 


5530.7793 


11 


279.3399 6209.4942 


J9 248.1858 


4901.6699 


U 


263.8938 


5541.7694 


89 


279.6017 6221.1389 


1 1 248.4476 


4912.0165 


1 


261.1556 


5552.7705 


1 


279.863-3 6232.7944 


2 \ 248.7094 


4922.3739 


2 


261.4174 


5563.7824 


2 


280.1253 6244.4608 


3 


248.9712 


4932.7423 


3 


264.6792 


5.374.8053 


3 


280.3871 6256.1382 


4 


249.2330 


4943.1215 


4 


264.9410 


5585.8390 


4 


280.6489 6267.8264 


5 


249.4948 


4953.5117 


5 


265.2028 


5.396.8837 


5 


280.9107 6279.52.36 


6 249.7566 


4963.9127 


6 


265.4646 


5607.9392 


6 


281.1725 6291.2356 


7 ; 250.0184 


4974.3247 


7 


265.7264 


5619.0057 


7 


281.4343 6302 9-366 


8 


250.2802 


4984.7476 


8 


26.3.9882 


5630.0831 


8 


281.6961 6314.6885 


9 


250.5420 


4995.1814 


9 


266.2.300 


5641.1714 


9 


281.9579 6326.4313 


10 


250.8038 


5005.6261 


10 


266.5118 5652.2706 


10 


282.2197 


6338.1850 


11 


251.0656 


5016.0817 


11 


266.7736 1 5663.3807 


''l 


282.4815 


6349.9496 






From Traiitwine's "Civil Eng^ineer's Pocket Book/' 



CIRCLES. 



TABIii: 3 OF CIRCI.es— (Continued). 
Diams in units and twelfths; as in feet and Incbes. 



Dia. 


Circumf. 


Area. 


Dia. 


Circumf. 


Area. 


Dia. 


Circumf. 


- Area. 


Ft.In. 


Feet. 


Sq. ft. 


Ft.In. 


Feet. 


Sq. ft. 


Ft.Iu. 


Feet. 


Sq. ft. 


90 


282.7433 


6361.7251 


93 5 1 293.4771 


6853.9184 


96 9 


303.9491 


7351. 7CS6 


1 


283.0051 


6373.5116 


6 293.7389 


6866.1471 


10 


304.2109 


78C4.4386 


2 


283.2669 


6385.3089 


7 294.0007 


6878.3917 


11 


304.471:7 


7377.1195 


3 


•-'83.52b7 


6397.1171 


8 \ 294.2625 


6890.6472 


97 


304.7345 


7:if9.8113 


4 


283.7905 


6l08.'.3r,3 


9 


294.5243 


6902.9135 


1 


304.9968 


7402.5140 


5 


284.0523 


6120.7663 


10 


294.7861 


6915.1908 


2 


305.2581 


7415.2277 


6 


284.3141 


6432.6073 


11 


295.0479 


6927.4791 


3 


305.5199 


7427.9522 


7 


284.5759 


6444.4592 


94 


295.3097 


6939.7782 


4 


305.7817 


7440.6877 


8 


284.8377 


6456.3220 


1 


295.5715 


6952.Ck882 


6 


306.0485 


7458.4340 


9 


285.0995 


6168.19.57 


2 


295.8333 


6964.4091 


6 


306.3053 


7466.1913 


10 


28.5.3613 


6180.0803 


3 ! 296.0951 


6976.7410 


7 


306.5671 1 7478.1595 


11 


285.0231 


6491 .97.. 8 


4 296.3569 


6989.0837 


8 


306.8289 


7491.7385 


11 


28.5 8849 


6503.882-: 


5 1:96.6187 


7001.4374 


9 


307.0907 


7504.52L5 


1 


286.1467 


6515.7995 


6 296.8805 


7018.8019 


10 


307.3525 


7517.329J 


2 


2S6 4085 


6527.727S 


7 297.1423 


7026.1774 


11 


307.6143 


7530.141'. 


3 


256.6703 


6.539.6669 


8 297.4041 


7038.5638 


98 


307.8761 


7542.9640 


4 


286.9321 


6551.6169 


9 


297.6659 


7050.9611 


1 


308.1379 


7555.7976 


5 


287.1939 


6563..5779 


10 


297.9277 


7063.3693 


2 


308.3997 


7568.0421 


6 


287.4557 


6575.5498 


11 


298.1895 


7075.7884 


3 


308.6615 


7.581.41,76 


7 


287.7175 


6587.5325 


96 1 298.4513 


70S8.2184 


4 308.92E8 


7594.3CS9 


8 


287.9793 


6.599..5262 


1 298.7131 


7100.6593 


5 


309.1851 


7607.2-n2 


9 


288 2411 


(5611.5308 


2 i 298.9749 


7113.1112 


6 


309.4469 


7620.1293 


10 


2885029 


6623.5163 


3 1 299.2367 


7125.5739 


7 


309.7087 


7638,0284 


11 


288 7647 


6635.5727 


4 299.4985 


7188.0476 


8 


809.9705 


764c .C384 


82 


289 0265 


6647.6101 


5 1 299.7603 


7150.5321 


9 


310.2323 


7658.8593 


1 


289.2883 


(;.r:9.()583 


6 ' 800.0221 


7163.0276 


10 


310.4941 


7671.7911 


2 


289..5501 


6671.7174 


7 ' 300.2839 


7175.5340 


11 


310.7559 


7684.7338 


3 


289.8119 


6683.7875 


8 300.5457 


7188.0513 


99 


311.0177 


7697.6874 


4 


290.0737 


6695.8684 


9 300.8075 


7200.5794 


1 


311.2795 


7710.6519 


5 


290.3355 


6707.9603 


10 301.0693 


7213.1185 


2 


SllMlS 


7723.6274 


6 


290.5973 


6720.0630 


11 801.3311 


7225.6686 


3 


311.8031 


7736.61.37 


7 


290.8591 


6732.1767 


96 301.5929 


7238.2295 


4 


312.0649 


7749.6109 


8 


■291.1209 


6744 3013 


1 301.8547 


7250.8013 


6 


312.8267 


7762.6191 


9 


291.3827 


6756 436s 


2 302.1165 


7263.8840 


6 


312.5885 


7775.6882 


10 


291.6 145 


67C8.5832 


3 802.3783 


7275.9777 


7 


312.8503 


7788.6681 


11 


291.9063 


6780.7405 


4 302.6401 


7288.5822 


8 


313.1121 


7801.7090 


«3 


292.1681 


6792.9087 


5 302.9019 


7301.1977 


9 


318.8739 


7814.7608 


1 


2924299 


6805.0878 


6 308.1637 


7318.8240 


10 


313.6357 


7827.8235 


2 


292.6917 


6817.2779 


7 303.4255 


7826.4613 


11 


813.8975 


7840.8971 


3 


292.9535 


6829.4788 


8 303.6873 


7839.1095 


100 


314.1593 


7853.9816 


4 


293.2153 


6&41-.6907 


1 




i 







Cirennifcrences in feet 


, ivhen tlie d 


iam contains fractions 




oi 


ait inch. See similar prucess. 


pl77 




Biam. 


Ciicumf. , L)i:tni, 


Circumf, Diam, 


Circumf, 


Diam, 


Circumf, 


Diam, 


Circumf, 


iBch. 


foot 

.004091 


Inch 

7-32 


foot 

.057269 


Inch 

27-64 


foot. 

.110447 


Inch. 

5-8 


foot. 


inch. 

53-64 


foot. 


1-64 


.163625 


.216803 


1-32 


.0081. SI 


1.5-64 


.061359 


7-16 


.114537 


41-64 


.167715 


27-32 


.220.^93 


3-64 


.012272 


'4 


.065450 


29-64 


.1186-'8 


21-32 


.171806 


55-64 


.224984 


1-16 


.016362 


17-64 


.069540 


15-32 


.122718 


43-64 


.176896 


7-8 


.229074 


5-64 


.020453 


9-32 


.073631 


31-64 


.126809 


11-16 


.179987 


57-64 


.233 16f 


3-32 


.024544 


19-64 


.077722 


M 


.130900 


45-64 


.184078 


29-32 


.237256 


7-64 


.028634 


5-16 


.081812 


3.3-64 


.134990 


23-82 


.188168 


59-64 


.241346 


% 


.032725 


21-64 


.085903 


17-32 


.139081 


47-64 


.192259 


15-16 


.245437 


9-64 


.036^16 


11-32 


,089994 


35-64 


.143172 


% 


.196350 


61-64 


.249528 


5-32 


.040906 


23-64 


.094084 


9-16 


.147262 


49-64 


.200440 


31-32 


.253618 


11-6 + 


.044997 


% 


.098175 


.37-64 


.151353 


25-32 


.204531 


63-64 


.257709 


3-16 


.049087 


25-04 


.102265 


19-32 


.155443 


51-64 


.208621 


1 


.261799 


13-64 


.<t53178 


13-32 


.106356 


39-64 


.1595.34 13-16 


.212712 







TABLE NO. 74. 185 

From Trautwine^s ** Civil Eng^ineer^'s Pocket Book/* 



SQUARE AND CUBE ROOTS. 



Sqnare Roots and €ube Roots of Numbers from .1 to 2S. 




















No 


errors. 


No. 


Square. 


! 

' Cube. 


Sq. Rt. 


1 

1 C. Bt. 


No. 


Sq. Rt. 


C.Rt. 


No. 


Sq. Rt. 


C.Rt. 


.1 


.01 


.001 


.316 


.464 


.7 


2.387 


1.786 


.4 


3.661 


2.375 


.15 


.0225 


.0034 


,387 


.531 


.8 


2.408 


1.797 


.6 


3.688 


2.387 


.2 


.04 


.008 


.447 


.585 


.9 


2.429 


1.807 


.8 


3.715 


2.399 


.25 


.0625 


.0156 


.500 


.630 


6. 


2.449 


1.817 


14. 


3.742 


2.410 


.3 


.09 


.027 


.548 


.669 


.1 


2.470 


1.827 


.2 


3.768 


2.422 


.35 


.1225 


.0429 


.592 


.705 


.2 


2.490 


1.837 


.4 


3.795 


2.433 


.4 


.16 


.064 


.633 


.737 


.3 


2.510 


1.847 


.6 


3.821 


2.444 


.45 


.2025 


.0911 


.671 


.766 


.4 


2.530 


1.857 


.8 


3.847 


2.455 


.5 


.25 


.125 


.707 


.794 


.5 


2.550 


1.866 


15. 


3.873 


2.466 


.55 


.3025 


.1664 


.742 


.819 


.6 


2.569 


1.876 


.2 


3.899 


2.477 


.6 


.36 


.216 


.775 


.843 


.7 


2.588 


1.885 


.4 


3.924 


2.488 


.65 


.4225 


.2746 


.806 


.866 


.8 


2.608 


1.895 


.6 


3.950 


2.499 


.7 


.49 


.343 


837 


.888 


.9 


2.627 


1.904 


.8 


3.975 


2.509 


.75 


.5625 


.4219 


.866 


.909 


7. 


2.646 


1.913 


16. 


4. 


2.520 


.8 


.64 


.512 


.894 


.928 


.1 


2.665 


1.922 


.2 


4.025 


2.530 


.85 


.7225 


.6141 


.922 


.947 


.2 


2.683 


1.931 


.4 


4.050 


2.541 


.9 


.81 


.729 


.949 


.965 


.3 


2.702 


1.940 


.6 


4.074 


2.551 


.95 


.9025 


.8574 


.975 


.983 


.4 


2.720 


1.949 


.8 


4.099 


2.561 


1. 


1.000 


1.000 


1.000 


1.000 


.5 


2.739 


1.957 


17. 


4.123 


2.571 


.05 


1.103 


1.158 


1.025 


1.016 


.6 


2.757 


1.966 


.2 


4.147 


2.581 


1.1 


1.210 


1.331 


1.049 


1.032 


.7 


2.775 


1 975 


.4 


4.171 


2.591 


.15 


1.323 


1.521 


1.072 


1.048 


.8 


2.793 


1.983 


.6 


4.195 


2.601 


1.2 


1.440 


1.728 


1.095 


1.063 


.9 


2.811 


1.992 


.8 


4.219 


2.611 


.25 


1.563 


1.963 


1.118 


1.077 


8. 


2.828 


2.000 


18. 


4.243 


2.621 


1.3 


1.690 


2.197 


1.140 


1.091 


.1 


2.846 


2.008 


.2 


4.266 


2.630 


.35 


1.823 


2.460 


1.162 


1.105 


.2 


2.864 


2.017 


.4 


4.290 


2 640 


1.4 


1.960 


2.744 


1.183 


1.119 


.3 


2.881 


2.025 


.6 


4.313 


2.650 


.45 


2.103 


3.049 


1.204 


1.132 


.4 


2.898 


2.0.33 


. .8 


4.336 


2.659 


1.5 


2.250 


3.375 


1.225 


1.145 


.5 


2.915 


2.041 


19. 


4.359 


2.668 


.55 


2.403 


3.724 


1.245 


1.157 


.6 


2.933 


2.049 


.2 


4.382 


2.678 


1.6 


2.560 


4.096 


1.265 


1.170 


.7 


2.950 


2.057 


.4 


4.405 


2.687 


.65 


2.723 


4.492 


1.285 


1.182 


.8 


2.966 


2.065 


.6 


4.427 


2.696 


1.7 


2.890 


4.913 


1.304 


1.193 


.9 


2.983 


2.072 


.8 


4.450 


2.705 


.75 


3.063 


5.359 


1.323 


1.205 


9. 


3. 


2.080 


20. 


4.472 


2.714 


1.8 


3.240 


5.832 


1..342 


1.216 


.1 


3.017 


2.088 


.2 


4.494 


2.723 


.85 


3.423 


6.332 


1.360 


1.228 


.2 


3.033 


2.095 


.4 


4.517 


2.732 


1.9 


3.610 


6.859 


1.378 


1.239 


.3 


3.050 


2.103 


.6 


4.539 


2.741 


.95 


3.803 


7.415 


1.396 


1.249 


.4 


3.066 


2.110 


.8 


4.561 


2.750 


». 


4.000 


8.000 


1.414 


1.260 


.5 


3.082 


2.118 


21. 


4.583 


2.759 


.1 


4.410 1 


9.261 


1.449 


1.281 


.6 


3.098 


2.125 


.2 


4.604 


2.768 


.2 


4.840* 1 


10.65 


1.483 


1.301 


.7 


3.114 


2.133 


.4 


4.626 


2.776 


.3 


5.290 I 


12.17 


1.517 


1.320 


.8 


3.130 


2.140 


.6 


4.648 


2.785 


.4 


5.760 1 


13.82 


1.549 


1.339 


.9 


3.146 


2.147 


.8 


4.669 


2.794 


.5 


6.250 


15.63 


1.581 


1.357 


10. 


3.162 


2.154 


22. 


4.690 


2.802 


.€ 


6.760 


17.58 


1.612 


1.375 


.1 


3.178 


2.162 


.2 


4.712 


2.810 


,7 


7.290 


19.68 


1.643 


1.392 


.2 


3.194 


2.169 


.4 


4.733 


2.819 


.8 


7.840 


21.95 


1.673 


1.409 


.3 


3.209 


2.176 


.6 


4.754 


2.827 


.9 


8.410 


24.39 


1.703 


1.426 


.4 


3.225 


2.183 


.8 


4.775 


2.836 


8. 


9. 


27. 


1.732 


1.442 


.5 


3.240 


2.190 


23. 


4.7V6 


2.844 


.1 


9.61 I 


29.79 


1.761 


1.458 


.6 


3.256 


2.197 


.2 


4.817 


2.852 


.2 


10.24 


32.77 


1.789 


1.474 


.7 


3.271 


2.204 


.4 


4.837 


2.860 


.3 


10.89 


.S5.94 


1.817 


1.489 


.8 


3.286 


2.210 


.6 


4.858 


2.868 


.4 


11.56 


39.30 


1.814 


1.504 


.9 


3..S02 


2.217 


.8 


4.879 


2.876 


.5 


12.25 


42.88 


1.871 


1.518 


11. 


3.317 


2.224 


24. 


4.899 


2.884 


.6 


12.96 


46.66 


1.897 


1.5.33 


.1 


3.332 


2.23J 


.2 


4.919 


2.892 


.7 


13.69 


50.65 


1.924 


1.547 


.2 


3.347 


2.287 


.4 


4.940 


2.900 


.8 


14.44 


54.87 


1.949 ' 


1.560 


.3 


3.362 


2.244 


.6 


4.960 


2.908 


.9 


15.21 i 


59.32 


1.975 


1.574 


.4 


3 376 


2.251 


.8 


4.980 


2.916 


4. 


16. 


64. 


2. 


1.587 


.5 


3.391 


2.257 


25. 


5. 


2.924 


.1 


16.81 1 


68.92 


2.025 


1.601 


.6 


3.406 


2.264 


.2 


5020 


2.932 


;2 


17.64 ! 


74.09 


2.049 


1 613 


.7 


3.421 


2.270 


.4 


5.040 


2.940 


.3 


18.49 


79.51 


2.074 


1.626 


.8 


3.4.35 


2.277 


.6 


5.060 


2.947 


.4 


19.36 


85.18 


2.098 


1.639 


.9 


3.450 


2283 


.8 


5.079 


2.955 


.5 


20.25 


91.13 


2.121 


1.651 


12. 


3.464 


2 289 


26. 


5099 


2.962 


.6 


21.16 


97.34 


2.145 


1.663 


.1 


3 479 


2.296 


.2 


5.119 


2.970 


.7 


22.09 


103.8 


2.168 


1.675 


/2 


3.493 


2.302 


4 


5.138 


2.978 


.8 


23.04 


110.6 


2.191 


1.687 


!3 


3.507 


2.308 


.6 


5.158 


2.985 


.9 


24.01 


117.6 


2.214 


1.69S 


.4 


3.521 


2.315 


.8 


5.177 


2.993 


6w 


25. 


125. 


2.236 


1.710 


.5 


3.5.36 


2.321 


27. 


5.196 


3.000 


.1 


26.01 


132.7 


2.258 


1.721 


.6 


3.550 


2.327 


.2 


5.215 


3.007 


.2 


27.04 


140.6 


2.280 


1.732 


.7 


3.564 


2.333 


.4 


5.235 


3.015 


.3 


28.09 


148.9 


2.302 


1.744 


.8 


3.578 


2 339 


.6 


5.254 


3.023 


.4 


29.16 


157.5 


2.324 


1.754 


.9 


3.592 


2.345 


.8 


5.273 


3.029 


.5 


3C.25 


166.4 


2.345 


1.765 


13. 


3.606 


2..S51 


28. 


5.292 


8.037 


.6 


31.36 


175-6 


2.366 


1.776 


.2 


3.6:^3 


2..363 


.2 


5.310 


3.0i4 



To find roots by logarithms see Pages 200 and 202. 



186 TABLE NO. 75. 

From Trantwine's ''Civil Engineer's Pocket Book." 



SQUARES, CUBES, AND ROOTS. 



TABI^E of Squares, Cabes, Sqnare Roots, and Cube Roots, 
of lumbers from 1 to 1000. 

Remark on the following Table. Wherever the effect of a fifth decimal in the roots would be t* 
kdd 1 to the fourth and final decimal in the table, the addition has heen made. No errors. 



No. 


Square. 


Cube. 


Sq. Bt. 


C. Rt. 


No. 


Square. 


Cube. 


Sq. B,t. 


C.Bt. 


1 


1 


1 


1.0000 


1.0000 


61 


3721 


226981 


7.8102 


3.9365 


2 


4 


8 


1.4142 


1.2599 


62 


3844 


238328 


7.8740 


3.9579 


3 


9 


27 


1.7321 


1.4422 


63 


3969 


250047 


7.9373 


3.9791 


4 


16 


64 


2.0000 


1.5874 


64 


4096 


262144 


8.0000 


4. 


5 


25 


125 


2.2361 


1.7100 


65 


4225 


274625 


8.0623 


4.0207 


« 


36 


216 


2.4495 


1.8171 


66 


4356 


287496 


8.1240 


4.0412 


•a 


49 


343 


2.6453 


1.9129 


67 


4489 


300763 


8.1854 


4.0615 


« 


64 


512 


2.8284 


2.0000 


68 


4624 


314432 


8.2462 


4.0817 


9 


81 


729 


3.0000 


2.0801 


69 


4761 


328509 


8.3066 


4.1016 


10 


100 


1000 


3.1623 


2.1544 


70 


4900 


343000 


8.3666 


4.1213 


11 


121 


1331 


3.3166 


2.2240 


71 


5041 


357911 


8.4261 


4.1403 


12 


144 


1728 


3.4641 


2.2894 


72 


5184 


373248 


8.4853 


4.1602 


13 


169 


2197 


3.6056 


2.3513 


73 


5329 


389017 


8.5440 


4.1793 


11 


196 


2744 


3.7417 


2.4101 


74 


5476 


405224 


8.6023 


4.1983 


15 


225 


3375 


3.8730 


2.4662 


75 


.5625 


421875 


8.6603 


4.2172 


16 


256 


4096 


4.0000 


2.5198 


76 


5776 


438976 


8.7178 


4.2358 


17 


289 


4913 


4.1231 


2.5713 


77 


5929 


456533 


8.7750 


4.2543 


18 


324 


5832 


4.2426 


2.6207 


78 


6084 


474552 


8.8318 


4.2727 


19 


361 


6859 


4.3589 


2.6684 


79 


6241 


493039 


8.8882 


4.2908 


20 


400 


8000 


4.4721 


2.7144 


80 


6400 


512000 


8.9443 


4.3089 


21 


441 


9261 


4.5826 


2.7589 


81 


6561 


531441 


9. 


4.3267 


22 


484 


10648 


4.6904 


2.8020 


82 


6724 


551368 


9.0554 


4.3445 


23 


529 


12167 


4.7958 


2.8439 


83 


6889 


571V87 


9.1104 


4.3621 


24 


576 


13824 


4.8990 


2.8845 


84 


7056 


592704 


9.1652 


4.3795 


25 


625 


15625 


5.0000 


2.9240 


85 


7225 


614125 


9.2195 


4.3968 


26 


676 


17576 


5.0990 


2.9625 


86 


7396 


636056 


9.2736 


4.4140 


27 


729 


19683 


5.1962 


3.0000 


87 


7569 


658503 


9.3274 


4.4310 


28 


784 


21952 


5.2915 


3.0366 


88 


7744 


631472 


9.3808 


4.4480 


29 


841 


24389 • 


5.3852 


3.0723 


89 


7921 


704969 


9.4340 


4.4647 


30 


900 


27000 


5.4772 


3.1072 


90 


8100 


729000 


9.4868 


4.4814 


31 


961 


29791 


5.5678 


3.1414 


91 


8281 


753571 


9.5394 


4.4979 


32 


1024 


32768 


5.6569 


3.1748 


92 


8464 


778688 


9.5917 


4.5144 


33 


1089 


35937 


5.7446 


3.2075 


93 


8649 


804357 


9.6437 


4.5307 


34 


1156 


39304 


5.8310 


3.2396 


94 


8836 • 


830584 


9.6954 


4.5468 


35 


1225 


42875 


5.9161 


3.2711 


95 


9025 


857375 


9.7468 


4.5629 


30 


1296- 


46656 


6.0000 


3..3019 


96 


9216 


884736 


9.7980 


4.5789 


37 


1369 


50653 


6.0828 


3.3322 


97 


9409 


912G73 


9.8489 


4.5947 


38 


1444 


54872 


6.1644 


3.3620 


98 


9604 


941192 


9.8995 


4.6104 


39 


1521 


59319 


6.2450 


3.3912 


99 


9S01 


970299 


9.9499 


4.6261 


40 


1600 


64000 


6.3246 


3.4200 


100 


10000 


1000000 


10. 


4.6416 


41 


1681 


68921 


■ 6.4031 


3.4432 


101 


10201 


1030301 


10.0499 


4.6570 


42 


1764 


74088 


6.4807 


3.4760 


102 


10404 


1061208 


10.0995 


4.6723 


43 


1849 


79507 


6.5574 


3.5034 


103 


10609 


1092727 


10.1489 


4.6375 


44 


1936 


85184 


6.6332 


3.5303 


104 


10816 


1124864 


10.1980 


4.7027 


45 


2025 


91125 


6.7082 


3.5569 


105 


11025 


1157625 


10.2470 


4.7177 


46 


2116 


97336 


6.7823 


3.5830 


106 


11236 


1191016 


10.2956 


4.7326 


47 


2209 


103823 


6.8557 


3.6088 


107 


11449 


1225043 


10.3441 


4.7475 


48 


2304 


110592 


6.9282 


3.6342 


108 


11664 


1259712 


10.3923 


4.7622 


49 


2401 


117649 


7.0000 


3.6593 


109 


11881 


1295029 


10.4403 


4.7769 


50 


2500 


125000 


7.0711 


3.6840 


110 


12100 


1331000 


10.4881 


4.7914 


61 


2601 


132651 


7.1414 


3.7084 


111 


12321 


1367631 


10.5357 


4.8059 


52 


2704 


140608 


7.2111 


3.7325 


112 


12544 


1404928 


10.5830 


4.3-203 


53 


2809 


148877 


7.2801 


3.7563 


113 


12769 


1U2897 


10.6301 


4.3346 


54 


2916 


157464 


7.3485 


3.7798 


114 


12996 


1481544 


10.6771 


4.848.8 


55 


3025 


166375 


7.4162 


3.8030 


115 


13225 


1520875 


10.7238 


4.8629 


56 


3136 


175616 


7.4833 


3.8259 


116 


13456 


1560896 


10.7703 


4.8770 


57 


3249 


185193 


7.5498 


3.8485 


117 


1.3689 


1601613 


10.8167 


4.8910 


58 


3364 


195112 


7.6158 


3.8709 


118 


13924 


164.3032 


10.8628 


4.9049 


69 


3481 


205379 


7.6811 


3.8930 


119 


14161 


1685159 


10.9087 


4.9187 


60 


3600 


216000 


7.7460 


3.9149 


120 


14400 


1728000 


10.9545 


4.9324 



TABLE NO. 75-CON. 187 

From Trantwine's "'Civil Engineer's Pocket Book." 



SQUARES, CUBES, AND ROOTS. 



TABIiE of Sqnares, Cubes. Square Roots. an<l Cube Roots, 
of Numbers from 1 to lOOO — {Conti.mkd } 



Ko. 


Square. 


Cube. 


8q. Rt. 


C. Rt. 


No. 


Square. 


Cube. 


Sq. Rt. 


C. Rt. 


121 


14641 


1771561 


11. 


4.946; 


186 


34596 


6434856 


13.6382 


5.7083 


122 


14884 


1815848 


11.0454 


4.9597 


187 


34969 


6539203 


13.6748 


5.7185 


123 


15129 


1860867 


11.0905 


4.9732 


188 


35344 


6644672 


13.7113 


5.7287 


124 


15376 


1906624 


11.1355 


4.9866 


189 


35721 


675126^9 


13.7477 


5.7388 


125 


15625 


1953125 


11.1803 


5. 


190 


36100 


6859000 


13.7840 


5.7489 


126 


15876 


2000376 


11.2250 


5.0133 


191 


36481 


6967871 


13.8203 


5.7590 


127 


16129 


204b38:! 


11.2694 


5.0265 


192 


36864 


7077888 


13.8564 


5.7690 


128 


16384 


2097152 


11.3137 


5.0397 


193 


37249 


7189057 


13.8924 


5.7790 


129 


16641 


2146n8a 


11.3578 


5.0528 


194 


37636 


7301384 


13.9284 


5.7890 


130 


16900 


2197000 


11.4018 


5.0658 


195 


38025 


7414875 


13.9642 


5.7989 


131 


17161 


2248091 


11.4455 


5.0788 


196 


38416 


7529536 


14. 


5.8088 


132 


17424 


2299968 


11.4891 


5.0916 


197 


38809 


7645373 


14.0357 


5.8186 


133 


17689 


2352637 


11.5326 


5.1045 


198 


39204 


7762392 


14.0712 


5.8285 


134 


1795S 


2406104 


11.5758 


5.1172 


199 


39601 


7880599 


14.1067 


5.8383 


135 


18225 


2460375 


11.6190 


5.1299 


200 


40000 


8000000 


14.1421 


5.8480 


136 


18496 


2515456 


11.6619 


5.1426 


201 


40401 


8120601 


14.1774 


5.8578 


137 


18769 


2571353 


ll.TOn 


5.1551 


202 


40804 


8242408 


14.2127 


5.8675 


138 


19044 


2628072 


11.7473 


5.1676 


203 


41209 


8,365427 


14.2478 


5.8771 


139 


19321 


2685619 


11.7898 


5.1801 


204 


41616 


8489664 


14.2829 


5.8868 


140 


19600 


2744000 


11.8322 


5.1925 


205 


42025 


8615125 


14.3178 


5.8964 


141 


19881 


2803221 


11.8743 


5.2048 


206 


42436 


8741816 


14.3527 


5.9059 


142 


20164 


2863288 


11.9164 


5.2171 


207 


42849 


8869743 


14.3875 


5.9155 


143 


20449 


2924207 


11.9583 


5.2293 


208 


43264 


8998912 


14.4222 


5.9250 


144 


20736 


2985984 


12. 


5.2415 


209 


43681 


9129329 


14.4568 


5.9345 


145 


21025 


3048625 


12.0416 


5.2536 


210 


44100 


9261000 


14.4914 


5.9439 


146 


21316 


3112136 


12.0830 


5.2656 


211 


44521 


9393931 


14.5258 


5.9538 


147 


21609 


3176523 


12.1244 


5.2776 


212 


44944 


9528128 


14.5602 


5.9627 


148 


21904 


3241792 


12.1655 


5.269G 


213 


45369 


9663597 


14.5945 


5.9721 


149 


22201 


3307949 


12.2066 


5.3015 


214 


45796 


9800344 


14.6287 


5.9814 


150 


22500 


3375000 


12.2474 


5.3133 


215 


46225 


9938375 


14.6629 


5.9907 


151 


22801 


3442951 


12.2882 


53251 


216 


46656 


10077696 


14.6969 


6. 


152 


23104 


3511808 


12.3288 


5.3368 


217 


47089 


10218313 


14.7309 


6.0092 


153 


23409 


3581577 


12.3633 


5.3485 


218 


47524 


10360232 


14.7648 


6.0185 


154 


2J716 


3652264 


12.4097 


5.3601 


219 


47961 


10503459 


14.7986 


6.0277 


155 


24025 


3723875 


12.4499 


5.3717 


220 


48400 


10648000 


14.8324 


6.0368 


156 


24336 


3796416 


12.4900 


5.3832 


221 


48841 


10793861 


14.8661. 


6.0459 


157 


24649 


3869893 


12.5300 


5.3947 


222 


49284 


10941048 


14.8997 


6.0550 


158 


24964 


3944312 


12.5698 


5.4061 


223 


49729 


11089567 


14.9332 


6.0641 


159 


25281 


4019679 


12.6095 


5.4175 


224 


50176 


11239424 


14.9666 


6.0732 


160 


25600 


4096000 


12.6«1 


5.4288 


225 


50625 


11390625 


15. 


6.0822 


161 


25921 


4173281 


12.6886 


5.4401 


226 


51076 


11543176 


15.0333 


6.0912 


162 


26244 


4251528 


12.7279 


5.4514 


227 


51529 


11697083 


15.0665 


6.1002 


163 


26569 


4330747 


12.7671 


5.4626 


228 


51984 


11852352 


15.0997 


6.1091 


164 


26896 


4410944 


12.8062 


5.4737 


229 


52441 


12008989 


15.1327 


6.1180 


165 


27225 


4492125 


12.8452 


5.4848 


230 


52900 


12167000 


15.1658 


6.1269 


166 


27556 


4574296 


12.8841 


5.4959 


231 


53361 


12326391 


15.1987 


6.1358 


167 


27889 


4657463 


12.9228 


5.5069 


232 


53824 


12487168 


15.2315 


6.1446 


168 


28224 


4741632 


12.9615 


5.5178 


233 


54289 


12649337 


15.2643 


6.1534 


169 


28561 


4826809 


13. 


5.5288 


234 


54756 


1281 2904 


15.2971 


6.1622 


170 


28900 


4913000 


13.0384 


5.,5397 


235 


55225 


12977875 


15.3297 


6.1710 


171 


29241 


5000211 


13.0767 


5.5505 


2.36 


55696 


13144256 


15.3623 


6.1797 


172 


29584 


508S448 


13.1149 


5.5613 


237 


56169 


13312053 


15.3948 


6.1885 


173 


29929 


5177717 


13.1529 


5.5721 


238 


56644 


13181272 


15.4272 


6.1972 


174 


30276 


5268024 


13.1909 


5.5H28 


239 


57121 


13651919 


15.4596 


6.2058 


175 


30625 


5359375 


13.2288 


5.5934 


240 


5760C 


1382i000 


15.4919 


6.2145 


176 


30976 


5451776 


13.2665 


5.6041 


241 


580S1 


13997521 


15.5242 


6.2231 


177 


31329 


5545233 


13.3041 


5.6147 


242 


5H564 


14172J88 


15.5563 


6.2317 


178 


31684 


5639752 


13.3417 


5.6252 


243 


59049 


14348907 


15. 5885 


6.2403 


179 


32041 


5735339 


13.3791 


5.6357 


244 


59536 


14526784 


15.6205 


6.2488 


180 


32400 


5832000 


13.4164 


5.6462 


245 


600-25 


14706125 


15.6525 


6.2573 


181 


32761 


5929741 


13.4536 


5.6567 


246 


60516 


14886936 


15.6844 


6.2658 


182 


33124 


6028568 


13.4907 


5.6671 


247 


61009 


15069223 


15.7162 


5.2743 


183 


83489 


6128487 


13.5277 


5.6774 


248 


61504 


15252992 


15.7480 


6.2828 


184 


33856 


6229504 


13.5647 


5.6877 


249 


62001 


15438249 


:5.:t97 


3.2912 


186 


34225 


6331625 


13.6015 


5.6980 


250 


62500 


15625000 


15.8114 


6.290C 



188 TABLE NO. 75— COX. 

From Trautwine's *• Civil Engineer's Pocket Book/ 



SQUARES, CUBES, AND KOOTS. 



TABIjE of Sc^nares, €nbes, Square Roots, and Cube Roots, 
of iVumbers from 1 to 1000 — (Coxtinued.) 



No. 


Square. 


Cube. 


Sq. B,t. 


cut. 


No^ 


Square. 


Cube. 


Sq. Rt. 


C. Rt. 


511 


261121 


133432831 


22.6053 


7.9948 


576 


331776 


191102976 


24. 


8.3203 


512 


262144 


134217728 


22.6274 


8. 


577 


332929 


192100033 


24.0208 


8.3251 


513 


263169 


135005697 


22.6495 


8.0052 


578 


334084 


193100552 


24.0416 


8.3300 


514 


264196 


135796744 


22.6716 


8.0104 


579 


335241 


194104539 


24.0624 


8.3348 


»5 


265225 


136590875 


22.6936 


8.0156 


580 


336400 


195112000 


24.0832 


^.3396 


516 


266256 


137388096 


22.7156 


8.0208 


581 


337561 


196122941 


24.1039 


8.3443 


517 


267289 


138188413 


22.7376 


8.0260 


582 


338724 


197137368 


24.1247 


8.3491 


518 


268324 


138991832 


22.7596 


8.0311 


583 


339889 


198155287 


24.1454 


8.3539 


519 


269361 


139798359 


22.7816 


8.0363 


584 


341056 


199176704 


24.1661 


8.3587 


520 


270400 


140608000 


22.8035 


8.0415 


585 


342225 


200201625 


24.1868 


8.3634 


521 


271441 


141420761 


22.8254 


8.0466 


586 


343396 


201230056 


24.2074 


8.3682 


522 


272484 


142236648 


22.8473 


8.0517 


587 


344569 


202262003 


24.2281 


8.3730 


523 


273529 


143055667 


22.8692 


8.0569 


588 


345744 


203297472 


24.2487 


8.377T 


524 


274576 


143877824 


22.8910 


8.0620 


589 


346921 


204336469 


24.2693 


8.3825 


525 


275625 


144703125 


22.9129 


8.0671 


590 


348100 


205379000 


24.2899 


8.3872 


526 


276676 


145531576 


22.9347 


8.0723 


591 


349281 


206425071 


24.3105 


8..3919 


527 


277729 


146363183 


22.9565 


8.0774 


592 


350464 


207474688 


24.3311 


8.3967 


528 


278784 


147197952 


22.9783 


8.0825 


593 


351649 


208527857 


24.3516 


8.4014 


529 


279841 


148035S89 


23. 


8.0876 


594 


352836 


209584584 


24..^721 


8.4061 


330 


280900 


148877000 


23.0217 


8.0927 


595 


354025 


210644875 


24.3926 


8.4108 


531 


281961 


149721291 


23.0434 


8.0978 


596 


355216 


211708736 


24.4131 


8.4155 


532 


283024 


150568768 


23.0651 


8.1028 


597 


356409 


212776J73 


24.4336 


8.4202 


533 


284089 


151419437 


23.08H8 


8.1079 


598 


357604 


213847192 


24.4540 


8.4249 


534 


285156 


152273304 


23.1084 


8.1130 


599 


358801 


214921799 


24.4745 


8.4296 


535 


286225 


153130375 


23.1301 


8.1180 


600 


360000 


216000000 


24.4949 


8.4343 


536 


287296 


153990656 


23.1517 


8.1231 


601 


361201 


217081801 


24.5153 


8.4390 


537 


288369 


154854153 


23.1733 


8.1281 


602 


362404 


218167208 


24.5357 


8.4437 


538 


289444 


155720872 


23.1948 


8.1332 


603 


36:3609 


219256227 


24.5561 


8.4484 


539 


290521 


156590819 


23.2164 


8.1382 


604 


364816 


220348864 


24.5764 


8.4530 


540 


291600 


157464000 


23.2379 


8.1433 


605 


366025 


221445125 


24.5967 


8.4577 


541 


292681 


158340421 


23.2594 


8.1483 


606 


367236 


222545016 


24.6171 


8.4623 


542 


293764 


159220088 


23.2809 


8.1533 


607 


368449 


223648543 


24.6374 


8.4670 


543 


294849 


160103007 


23.3024 


8.1583 


608 


369664 


224755712 


24.6577 


8.4716 


544 


295936 


160989184 


23.3238 


8.1633 


609 


370881 


225866529 


24.6779 


8.4763 


545 


297025 


161878625 


23.3452 


8.1683 


610 


372100 


226981000 


24.6982 


8.4809 


546 


298116 


162771336 


23.3666 


8.1733 


611 


373321 


228099131 


24.7184 


8.4856 


547 


299209 


163667323 


23.3880 


8.1783 


612 


374544 


229220928 


24.7388 


8.4902 


548 


300304 


164566592 


23.4094 


8.1833 


613 


375769 


230346;397 


24.7588 


8.4948 


549 


301401 


165469149 


23.4307 


8.1882 


614 


376.^96 


231475.544 


24.7790 


8.4994 


550 


302500 


166375000 


23.4521 


8.1932 


615 


378225 


232608375 


24.7992 


8.5040 


551 


303601 


167284151 


23.4734 


8.1982 


616 


379456 


233744896 


24.8193 


8.5086 


552 


304704 


168196608 


23.4947 


8.2031 


617 


380689 ■ 


2348»5113 


24.B395 


8.51.32 


553 


305809 


169112377 


23.5160 


8.2081 


618 


381924 


236029032 


24 8596 


8.5178 


554 


306916 


170031464 


23.5372 


8.2130 


619 


383161 


237176659 


24.8797 


8.5224 


555 


308025 


170953875 


23.5584 


8.2180 


620 


384400 


238328000 


24.8998 


8.5270 


556 


309136 


171879616 


23.5797 


8.2229 


621 


385641 


239483061 


24.9199 


8.5316 


557 


310249 


172808693 


23.6008 


8.2278 


622 


386884 


240641S48 


24.9399 


8.5362 


558 


311364 


173741112 


23.6220 


8.2327 


623 


388129 


241804367 


24.9600 


8.5408 


559 


312481 


174676879 


23.6432 


8.2377 


624 


389376 


242970624 


24.9S0O 


8.5453 


660 


313600 


175616000 


23.6643 


8.2426 


625 


390625 


244140625 


25. 


8.5499 


561 


314721 


176558481 


23.6854 


8.2475 


626 


391876 


245314376 


25.0200 


8.5544 


562 


315844 


177504328 


23.7065 


8.2524 


627 


393129 


246491883 


25.0400 


8.5590 


663 


316969 


178453547 


23.7276 


8.2573 


628 


394384 


247673152 


25.0599 


8.5635 


564 


318096 


179406144 


23.7487 


8 2621 


629 


395641 


248858189 


25.0799 


8.5681 


665 


319225 


180362125 


23.7697 


8.2670 


630 


396900 


250047000 


25.0998 


8.5726 


666 


320356 


181321496 


23.7908 


8.2719 


631 


.398161 


251239591 


25.1197 


8.5772 


667 


321489 


182284263 


23.8118 


8.2768 


632 


3994-'4 


25243.1968 


25.1396 


8.5^17 


568 


322624 


183250432 


23.8328 


8.2816 


633 


400689 


253K;H6137 


25.1595 


S.hHH-' 


569 


323761 


184220009 


23.8537 


8.2865 


6:U 


401956 


2.54rt40104 


25.1794 


8.5907 


570 


324900 


185193000 


23.8747 


8.2913 


635 


403225 


256047875 


25-1992 


8.5952 


571 


326041 


186169411 


23.8956 


8.2962 


636 


404496 


257259456 


25.2190 


8.5997 


672 


327184 


187149248 


23.9165 


8.3010 


637 


405769 


258474S53 


25.23«» 


8.6043 


573 


328329 


188132517 


23.9374 


8.3059 


638 


407044 


2596144072 


25.2587 


8.6088 


574 


329476 


189119224 


23.9583 


8.3107 


639 


40-^321 


260917119 


25.2784 


8.6132 


575 


330625 


190109375 


23.9792 


8.3155 


610 


409600 


262144000 


25.2982 


8.61T7 



TAIJLE NO. 75- CON. 189 

From Traut Winers '^ Civil Eng:iiieer*s Pocket Book/' 

SQUARES, CUBES, AND ROOTS. 



TABliE of Squares, Cubes, Square Roots, and Cube Roots, 
of Numbers from 1 to 1000 — (Continued.) 



No. 


Square. 


Cube. 


Sq. Rt. 


C. Rt 


No. 


Square. 


Cube. 


Sq. Rt. 


C. Rt. 


251 


i 63001 


15813251 


15.8430 


6..3010 


316 


99«56 


31554496 


17.7764 


6.'<113 


252 


! 63504 


16003008 


15.8745 


6.3164 


317 


100489 


31855013 


17.8045 


6.8185 


253 


64009 


16194277 


15.9060 


6.3247 


318 


101124 


32157432 


17.8326 


6.8256 


254 


64516 


16387064 


15.9374 


6.3330 


319 


101761 


32461759 


17.8606 


6.83-28 


255 


! 65025 


16581375 


15.9687 


6..3413 


320 


102400 


32768000 


17.8885 


6.8399 


256 


65536 


16777216 


16. 


6.3496 


321 


103041 


33076161 


17.9165 


6.8470 


257 


66049 


16974593 


16.0312 


6.3579 


322 


103684 


33386248 


17.9444 


6.8541 


258 


66564 


17173512 


16.0624 


6.3661 


323 


104329 


33698-267 


17.9722 


6.8612 


259 


67081 


17373979 


16.0935 


6.3743 


324 


104076 


340122-24 


18. 


6.86x3 


260 


67600 


17576000 


16.1245 


6.3825 


325 


105625 


343-28125 


18.0278 


6.8753 


261 


68121 


17779581 


16.1555 


6.3907 


326 


106276 


34645976 


18.0555 


6.88-24 


262 


68644 


1 798472'* 


16.1864 


6.398s 


327 


106929 


34965783 


18.0831 


6.8394 


263 


69169 


18)91+47 


16.2173 


6.4070 


328 


107584 


35-287552 


18.1108 


6.8964 


264 


69696 


18.(9^744 


16.2481 


6.4151 


329 


108241 


35611289 


18.1384 


6.9034 


265 


70225 


18609625 


16.2788 


6.4232 


330 


108900 


35937000 


18.16.59 


6.9104 


S66 


70756 


18821096 


16..3095 


6.4312 


331 


109561 


36-264691 


18.1934 


6.9174 


267 


71289 


1903416:^ 


16.3401 


6.4393 


332 


110224 


36594368 


18.2209 


6.9244 


268 


71824 


1924883*2 


16.3707 


6.4473 


333 


110889 


36926037 


18.2483 


6.9313 


269 


72361 


19465109 


16.4012 


6.4553 


334 


111556 


37-259704 


18.2757 


6.9382 


270 


72900 


19683000 


16.4317 


6.4633 


335 


112225 


37595375 


18.3030 


6.9451 


271 


73441 


19902511 


16.4621 


6.4713 


336 


112896 


37933056 


18.3303 


6.9521 


272 


73984 


20123648 


16.4924 


6.4792 


337 


113569 


38272753 


18.3576 


6.9589 


273 


74529 


20346417 


16.5227 


6.4872 


338 


114244 


38614472 


18.3848 


6.9658 


274 


75076 


20570824 


16.5529 


6.4951 


339 


114921 


38958219 


18.4120 


6.97-27 


275 


75625 


20796875 


16.5831. 


6.5030 


340 


115600 


39304000 


18.4391 


6.9795 


276 


76176 


21024576 


16.6132 


6.5108 


341 


116281 


.39651821 


18.4662 


6.9864 


277 


76729 


21253933 


16.6133 


6.5187 


342 


116964 


40001688 


18.4932 


6.9932 


278 


77284 


21484952 


16.6733 


6.5265 


343 


117649 


40353607 


18.5203 


7. 


279 


778 n 


21717639 


16.7033 


6.5343 


3U 


118336 


40707584 


18.5472 


7.0068 


280 


78400 


21952000 


16.7332 


6.5421 


345 


119025 


41063625 


18.5742 


7.0136 


281 


78961 


22188011 


16.7631 


6.5499 


346 


119716 


41421736 


18.6011 


7.0203 


282 


79524 


22425768 


16.7929 


6.5577 


347 


120409 


41781923 


13.6279 


7.0271 


283 


80089 


22665187 


16.8226 


6.5654 


348 


121104 


42144192 


18.6548 


7.0338 


384 


80656 


22906304 


16.8523 


6.5731 


349 


121801 


42508549 


18.6815 


7.0406 


285 


81225 


23149125 


16.8819 


6.5808 


350 


122500 


42875000 


18.7083 


7.0473 


286 


81796 


23393656 


16.9115 


6.5885 


351 


123201 


43243551 


18.7350 


7.0540 


287 


82.i69 


23639^03 


16.9411 


6.5962 


352 


123904 


43614-208 


18.7617 


7.0607 


288 


82944 


23887872 


16.9706 


6.6039 


353 


124609 


43986977 


18.7883 


7.0674 


289 


83521 


24137569 


17. 


6.6115 


354 


125316 


44361864 


18.8149 


7.0740 


250 


84100 


24389000 


17.0294 


6.6191 


355 


126025 


44738875 


18.8414 


7.0807 


291 


84681 


24642171 


17.0587 


6.6267 


356 


126736 


45118016 


18.8680 


7.0873 


292 


85264 


24897088 


17.0880 


6.6343 


357 


127449 


45499293 


18.8944 


7.0940 


293 


85819 


25153757 


17.1172 


6.6419 


358 


128164 


45882712 


18.9-209 


7.1006 


291 


86136 


25412184 


17.1464 


6.6494 


359 


128881 


46268279 


18.9473 


7.107J 


295 


87025 


25672375 


17.1756 


6.6569 


360 


129600 


46656000 


18.9737 


7.1133 


296 


87616 


25934336 


17.2017 


6.6644 


.361 


1.30321 


47045881 


19. 


7.1204 


2:^7 


88209 


26198073 


17.2337 


6.6719 


362 


131044 


474379-28 


19.0263 


7.1269 


298 


88804 


2646;J592 


17.2627 


6.6794 


363 


131769 


47832147 


19.05-26 


7.1335 


299 


89401 


26730899 


17.2916 


6.6869 


364 


132496 


48228544 


19.0788 


7.1400 


300 


90000 


27000000 


17.3205 


^6943 


365 


133225 


48627125 


19.1050 


7.1466 


301 


90601 


27270901 


17.3494 


6.7018 


366 


133956 


49027896 


19.1311 


. 7.15.31 


302 


91204 


27543608 


17. .3781 


6.7092 


367 


134689 


49430863 


19.1572 


7.1596 


303 


91809 


27818127 


17.4069 


6.7166 


368 


135424 


49836032 


19.1833 


7.1661 


304 


9241 fi 


28094464 


17.4356 


6.7240 


369 


1.36161 


50243409 


19.2094 


7.17-26 


305 


9;1025 


28372625 


17.4642 


6.7313 


370 


136900 


50653000 


19. -2354 


7.1791 


306 


93636 1 


28652616 


17.4929 


6.7.387 


371 


137641 


51064811 


19.2614 


7.1855 


307 


94249 


28:>34143 


17.5214 


6.7460 


372 


138:iK4 


51478848 


19.2873 


7.19-20 


308 


94864 


2:^218112 


17.5499 


6.7533 


373 


139129 


51895117 


19.31.32 


7.1984 


309 


95481 1 


29503629 


17.5781 


6.7606 


374 


1.39876 


523136-Z4 


19.3391 


7. -2048 


310 


96100 


29791000 


17.6068 


6.7679 


375 


140625 


5-2734375 


19.3649 


7.-21 1-i 


311 


96721 


30080231 


17.6352 


6.7752 


376 


141376 


53157376 


19.3907 


7.2177 


312 


97344 < 


30371328 


17.6635 


6.7824 


377 


1421-29 


535S-2633 


19.4165 


7.2240 


313 


97969 


30664-297 


17.6918 


6.7897 


378 


1428M4 


54010152 


19.4422 


7.2304 


314 


98596 ! 


30959144 


17.7200 


6.7969 


379 


143641 


544:19939 


19.4679 


7.236* 


S15 


992.:5 ! 


31255875 


li.Hoi 


6.8041 


380 


144400 < 


5487-2000 


19.4936 


T.243I 



190 TBALE NO. 75— CON. 

From Traiitwine*s "Civil Engineer's Pocket Book.' 



SQUARES, CUBES, AND ROOTS. 



TABIiE of i^qnares. Cubes, Sqnare Roots, and Cube Roots, 
of Numbers from 1 to 1000 — (Continued.) 



No. 


Square. 


Cube. 


Sq. Kt. 


cut. 


No. 


Square. 


Cube. 


Sq. Rt. 


C. Bt. 


381 


145161 


55306341 


19.5192 


7.2495 


446 


198916 


88716536 


21.1187 


7.6403 


382 


145924 


55742968 


19.5448 


7.2558 


447 


199809 


89314623 


21.1424 


7.6460 


383 


146689 


56181887 


19.5704 


7.2622 


448 


200704 


89915392 


21.1660 


7.6517 


384 


147456 


56623104 


19.5959 


7.2685 


449 


201601 


90518849 


21.1896 


7.6574 


385 


148225 


57066625 


19.6214 


7.2748 


450 


202500 


91125000 


21.2132 


7.6631 


386 


148996 


57512456 


19.6469 


7.2811 


451 


203401 


917,33851 


21.2368 


7.6688 


387 


149769 


57960603 


19.6723 


7.2874 


452 


204304 


92345408 


21.2603 


7.6744 


388 


150544 


58411072 


19.6977 


7.2936 


453 


205209 


92959677 


21.2838 


7.6801 


389 


151321 


58863869 


19.7231 


7.2999 


454 


206116 


93576664 


21.3073 


7.6857 


390 


152100 


59319000 


19.7484 


7.3061 


455 


207025 


941%375 


21.3307 


7.6914 


391 


152881 


59776471 


19.7737 


7.3124 


456 


207936 


94818816 


21.3542 


7.69TO 


392 


153664 


60236288 


19.7990 


7.3186 


457 


208849 


95443993 


21.3776 


7.7026 


393 


154449 


60698457 


19.8242 


7.3248 


458 


209764 


96071912 


21.4009 


7.7082 


394 


155236 


61162984 


19.8494 


7.3310 


459 


210681 


96702579 


21.4243 


7.7138 


395 


156025 


61629875 


19.8746 


7.3372 


460 


211600 


97336000 


21.4476 


7.7194 


396 


156816 


62099136 


19.8997 


7.3434 


461 


212521 


97972181 


21.4709 


7.7250 


397 


157609 


62570773 


19.9249 


7.3496 


462 


213444 


98611128 


21.4942 


7.7306 


398 


158404 


63044792 


19.9499 


7.3558 


463 


214369 


99252847 


21.5174 


7.7362 


399 


159201 


63521199 


19.9750 


7.3619 


464 


215296 


93897344 


21.5407 


7.7418 


400 


160000 


64000000 


20. 


7.3681 


465 


216225 


100544625 


21.5639 


7.747» 


401 


160801 


64481201 


20.0250 


7.3742 


466 


217156 


101194696 


21.5870 


7.7529 


402 


161604 


64964808 


20.0499 


7.3803 


467 


218089 


101847563 


21.6102 


7.7584 


403 


162409 


65450827 


20.0749 


7.3864 


468 


219024 


102503232 


21.6333 


7.7639 


404 


163216 


65939264 


20.0998 


7.3925 


469 


■ 219961 


103161709 


21.6564 


7.7695 


405 


164025 


66430125 


20.1246 


7.3986 


470 


220900 


103823000 


21.6795 


7.7750 


406 


164836 


66923416 


20.1494 


7.4047 


471 


221841 


104487111 


21.7025 


7.780& 


407 


165649 


67419143 


20.1742 


7.4108 


472 


222784 


105154048 


21.7256 


7.7860 


408 


166464 


67917312 


20.1990 


7.4169 


473 


223729 


105823817 


21.7486 


7.7915 


409 


167281 


68417929 


20.2237 


7.4229 


474 


224676 


106496424 


21.7715 


7.7970 


410 


168100 


68921000 


20.2485 


7.4290 


475 


225625 


1071V1875 


21.7945 


7.8025 


411 


168921 


69426531 


20.2731 ' 


7.4350 


476 


226576 


107850176 


21.8174 


7.8079 


412 


169744 


69934528 


20.2978 


7.4410 


477 


227529 


108531333 


21.8403 


7.8134 


413 


170569 


70444997 


20.3224 


7.4470 


478 


228484 


109215352 


21.8632 


7.8188 


414 


171396 


70957944 


20.3470 


7.4530 


479 


229441 


109902239 


21.8861 


7.8243 


415 


172225 


71473375 


20.3715 


7.4590 


480 


230400 


110592000 


21.9089 


7.8297 


416 


173056 


71991296 


20.3961 


7.4650 


481 


231361 


111284641 


21.9317 


7.8.352 


417 


173889 


72511713 


20.4206 


7.4710 


482 


232324 


111980168 


21.9545 


7.8406 


418 


174724 


73034632 


20.4450 


7.4770 


483 


233289 


112678587 


21.9773 


7.8460 


419 


175561 


73560059 


20.4695 


7.4829 


484 


234256 


113379904 


22. 


7.8514 


420 


176400 


74088000 


20.4939 


7.4889 


485 


235225 


114084125 


22.0227 


7.8568 


421 


177241 


74618461 


20.5183 


7.4948 


486 


236196 


114791256 


22.0454 


7.8622 


422 


178084 


75151448 


20.5426 


7.5007 


487 


237169 


115501303 


22.0681 


7.8676 


423 


178929 


75686967 


20.5670 


7.5067 


488 


238144 


116214272 


22.0907 


7.8730 


424 


179776 


76225024 


20.5913 


7.5126 


489 


239121 


116930169 


22.1133 


7.8784 


425 


180625 


76765625 


20.6155 


7.5185 


490 


240100 


117649000 


22.1359 


7.8837 


426 


181476 


77308776 


20.6398 


7.5244 


491 


241081 


118370771 


22.1585 


7.8891 


427 


182329 


77854483 


20.6640 


7.5302 


492 


242064 


119095488 


22.1811 


7.8944 


428 


183184 


78402752 


20.6882 


7.5361 


493 


243049 


119823157 


22.2036 


7.8998 


429 


184041 


78953589 


20.7123 


7.5420 


494 


244036 


129553784 


22.2261 


7.9051 


430 


184900 


79507000 


20.7364 


7.5478 


495 


245025 


121287375 


22.2486 


7.910& 


431 


185761 


80062991 


20.7605 


7.5537 


496 


246016 


122023936 


22.2711 


7.9158 


432 


• 186624 


80621568 


20.7846 


7.5595 


497 


247009 


122763473 


22.2935 


7.9211 


433 


187489 


81182737 


20.8087 


7.5654 


498 


248004 


123505992 


22.3159 


7.9264 


434 


188356 


81746504 


20.8327 


7.5712 


499 


249001 


124251499 


22.3383 


7.9317 


435 


189225 


82312875 


20.8567 


7.5770 


500 


250000 


125000000 


22.3607 


7.9370 


436 


190096 


82881856 


20.8806 


7.5828 


501 


251001 


125751501 


22.3830 


7.9423 


437 


190969 


83453453 


20.9045 


7.5886 


502 


252004 


12650600fc 


22.4054 


7.9476 


438 


191844 


84027672 


20.9284 


7.5944 


503 


253009 


127263527 


22.4277 


7.9528 


439 


192721 


84604519 


20.9523 


7.6001 


504 


254016 


128024061 


22.4499 


7.9581 


440 


193600 


85184000 


20.9762 


7.6059 


505 


255025 


128787623 


22.4722 


7.9634 


441 


194481 


85766121 


21. 


7.6117 


506 


256036 


129554216 


22.4944 


7.9686 


442 


195364 


86350888 


21.0238 


7.6174 


507 


257049 


130323843 


22.5167 


7.9739 


443 


196249 


86938307 


21.0476 


7.6232 


508 


258064 


131096515 


22.5389 


7.9791 


444 


197136 


8752a384 


21.0713 


7.6289 


509 


259081 


13187222S 


22.5610 


7.9843 


446 


198025 


88121125 


21.0950 


7.6346 


510 


260100 


13265100C 


22.5832 


I 7.9896 



TABLE NO. 75-CON. 191 

Front Traiitwine'!« "Civil I:Iiig:ineer\s Pocket Book.'* 



SQUARES, CUBES, AND ROOTS. 



TABLE of Squares, Cnbes, Square Roots, and €nbe Roots, 
of Numbers from 1 to 1000 — (Continued.) 



No. 


Sciuare. 


Cube. 


Sq. Ht. 


cut. 


No. 


Square. 


Cube. 


Sq. Bt. 


C. Rt. 


641 


410881 


263374721 


25.3180 


8.6222 


706 


498436 


351895816 


26.5707 


8.9043 


612 


412164 


264609288 


25.;3377 


8.6267 


707 


499849 


.353:393243 


26.5895 


8.9085 


613 


413449 


265847707 


25.3574 


8.6312 


708 


501264 


354894912 


2(5.6083 


8.9127 


64 1 


414736 


267089984 


25.3772 


8.6357 


709 


50268! 


3564008;;9 


26.6271 


8.9169 


&15 


416025 


268336125 


25.:3969 


8.6401 


710 


504100 


357911000 


26.6458 


8.9211 


646 


417316 


269586136 


25.4165 


8.6446 


711 


505521 


359425431 


26.6646 


8.9253 


647 


418309 


270810023 


25.4362 


8.6490 


712 


506944 


360944128 


26.6833 


8.9295 


61« 


419^04 


272097792 


25.4558 


8.65:35 


713 


508369 


362467097 


26.7021 


8.9337 


619 


421201 


273359149 


25.4755 


8.6579 


714 


509796 


363994344 


26.7208 


8.9378 


660 


422500 


?74625000 


25.4951 


8.6624 


715 


511225 


' 365525875 


26.7395 


8.942C 


651 


423S01 


275894451 


25.5147 


8.6668 


716 


512656 


367061696 


26.7582 


8.9462 


652 


425101 


277167808 


25.5343 


8.6713 


717 


514089 


368601813 


26.7769 


8.9503 


€53 


426109 


278445077 


25.5539 


8.6757 


718 


515524 


370146232 


26.7955 


8.9545 


651 


427716 


279726264 


25.5734 


8.6801 


719 


516361 


371694959 


26.8142 


8.9587 


655 


429025 


281011375 


25.5930 


8.6845 


720 


518400 


373248000 


26.8328 


8.9628 


656 


430338 


282300416 


25.6125 


8.6890 


721 


519841 


374805361 


26.8514 


8.9670 


657 


431619 


283593393 


25.6320 


8.6934 


722 


621284 


37636704S 


26.8701 


8.9711 


658 


432964 


284890312 


25.6515 


8.6978 


723 


522729 


377933067 


26.8887 


8.9752 


659 


431281 


2861'JJ179 


25.6710 


8.7022 


724 


524176 


379503424 


26.9072 


8. 9794 


660 


435600 


287496000 


25.6905 


8.7066 


725 


525625 


381078125 


26.9258 


8.9835 


6C1 


436921 


288801781 


25.7099 


8.7110 


726 


527078 


382657176 


26.9444 


8.9876 


66-i 


438244 


290117528 


25.7294 


8.7154 


727 


528529 


3842405S3 


26.9629 


8.9918 


66:3 


439569 


291434247 


25.7488 


£.7198 


728 


529984 


385S28352 


26.9815 


8.9959 


664 


440396 


292751914 


25.7682 


8.7241 


729 


531441 


3H74 20489 


27. 


9. 


665 


442225 


294079625 


25.7876 


8.7285 


730 


5329CK) 


[ 389017000 


27.0185 


9.0041 


686 


443556 


295408296 


25.8070 


8.7329 


731 


534361 


390617891 


27.0370 


9.0082 


667 


444889 


296740963 


25.8263 


8.7373 


732 


535824 


392223168 


27.0555 


9.0123 


668 


416224 


298077632 


25.8457 


8.7416 


733 


537289 


393832837 


27.0740 


9.0164 


669 


447X61 


299418309 


25.8650 


8.7460 


7:34 


538756 


395446904 


27.0924 


9.0205 


670 


44S900 


300763000 


25.8844 


8.7503 


735 


540225 


397065375 


27.1109 


9.0246 


671 


450241 


302111711 


25.9037 


S.7547 


736 


541696 


398688256 


27.1293 


9.0287 


67-i 


451584 


303464448 


25.9230 


8.7590 


737 


543169 


400315553 


27.1477 


9.0328 


673 


452929 


304821217 


25.9422 


8.7634 


738 


544644 


401947272 


27.1662 


9.0369 


674 


454276 


806182024 


25.S615 


8.7677 


739 


546121 


403583419 


27.1816 


9.0410 


675 


455625 


307546875 


25.S808 


8.7721 


740 


547600 


405224000 


27.2029 


9.0450 


676 


45C976 


308915776 


26. 


8.7764 


741 


5^9081 


406869021 


27.2213 


9.0491 


677 


45B329 


310288733 


26.0192 


8.7807 


742 


550564 


40S518488 


27.2397 


9.0532 


678 


459684 


311665752 


26.0.384 


8.7850 


743 


552049 


410172407 


27.2580 


9.0572 


679 


461041 


313046839 


26.0576 


8.7893 


744 


553536 


411830784 


27.2764 


9.0613 


680 


462100 


314432000 


26.0768 


8.7937 


745 


555025 


413493625 


27.2947 


9.0654 


6.S1 


463761 


315821241 


26.0960 


8.7980 


746 


556516 


415160936 


27.3130 


9.0694 


682 


465124 


317214568 


26.1151 


8.8023 


747 


558009 


416832723 


27.3313 


9.07:35 


6B3 


466489 


318611987 


26.1:343 


8.8066 


748 


559504 


418508992 


27.3496 


9.0775 


6J54 


467a56 


320013504 


26.1534 


8.8109 


749 


561001 


4201S9749 


27.3679 


9.0816 


685 


469225 


321419125 


26.1725 


8.8152 


750 


562500 


421875000 


27.:3S61 


9.0856 


686 


470596 


3228288561 


26.1916 


8.8194 


751 


564001 


423564751 


27.4044 


9.0896 


687 


471969 


324242703 


26.2107 


8.8237 


752 


565504 


425259008 


27.4226 


9.0937 


«88 


473344 


325660672 


26.2298 


8.8280 


753 


567009 


426957777 


27.4408 


9.0977 


689 


474721 


327082769 


26.2488 


8.8323 


754 


568513 


428661064 


27.4591 


9.1017 


690 


476100 


328509000 


26.2679 


8.83G6 


755 


570025 


430368875 


27.4773 


9.1057 


691 


477481 


329939371 


26.2869 


8.8408 


756 


571536 


432081216 


27.4955 


9.1098 


692 , 


478864 


33ri73HS8 


26.30.59 


8.8451 


757 


573049 


433798093 


27 5i:36 


9.11:38 


693 


480219 


33; .81 2557' 


26.3249 


8.8493 


758 


574564 


435519512 


27.5318 


9.1178 


694 


4S1636 


3:^4255384 


26.34:39 


8.8536 


759 


576081 


437245479 


27.5500 


9.1218 


695 1 


483025 


S35702375 


26.3629 


8.8578 


760 


577600 


438976000 


27.5681 


9.1258 


696 1 


481416 


3371535:36' 


26.3818 


8.8621 


761 


579121 


440711081! 


27.5862 


9.1293 


697 


485809 


338608873 


26.4008 


8.8663 


762 


580644 


442450728 


27.6043 


9.1:5:38 


698 


4H7204 


340068392 


26.4197 


8.8706 


763 


582169 


444194947 


27.6225 


9.1:378 


699 


4H«()l)l 


311532099 


26.4386 


8.8748 


764 i 


583696 


44594;!744 


27.6405 


9.1418 


700 


490000 


343000000 


26.4575 


8.8790 


765 


585225 


447697125 


27.6586 


9.1458 


70' 


431401 


344472101 


26.47f 


8.88:33 


766 


586756 


449455096 


27.6767 


9.1498 


7i>2 


492S04 


34594K408 


26.49.5a 


8.8875 


767 . 


588289 


451217663 


27.6948 


9.1537 


70.) 


49420J 


347428927 


i6.5141 


8 8917 


768 


589824 


452984832 


27.7128 


9.1577 


704 


4.^56 i6 


34891:3664 


26.5330 


8.8959 


769 


591361 


4547.56609 


27.7:308 


9.1617 


ZOo 


497025 1 


350402625 


26.5518 1 


8.9001 


770 


592900 


4565330091 


27.7489 


9.1657 



192 . TABLE NO. 75— CON. 

From Trautwine's *>* Civil Engineer's Pocket Book.' 



SQUARES, CUBES, AND ROOTS. 



TABLE of Squares, Cubes, Square Roots, and Cube Roots, 
of EFumbers from 1 to 1000 — (Continued.; 



No. 


i 
Square. 


Cube. 


Sq. Rt. 


C. Kt. 


No. 


Square. 


Cube. 


Sq. Rt. 


C. Rt. 


771 


594441 


458314011 


27.7669 


9.1696 


836 


698896 


584277056 


28.9187 


9.4204 


772 


595984 


i 4*0099646 


27.7849 


9.1736 


837 


700569 


586376253 


28.9310 


9.4241 


773 


597529 


461889917 


27.8029 


9.1775 


838 


702244 


588480472 


28.9482 


9.427» 


774 


599076 


1 463684824 


27.8209 


9.1815 


839 


703921 


590589719 


28.9655 


9.4316 


775 


600625 


I 465484375 


27.8388 


9.1855 


840 


705600 


592704000 


28.9828 


9.4354 


776 


602176 


467288576 


27.8568 


9.1894 


841 


707281 


594823321 


29. 


9.439t 


777 


603729 


469097433 


27.8747 


9.1933 


842 


708964 


596947688 


29.0172 


9.442» 


778 


605284 


! 470910952 


27.8927 


9.1973 


843 


710649 


599077107 


29.0.345 


9.4466 


779 


606841 


472729139 


27.9106 


9.2012 


844 


712336 


601211584 


29.051 1 


9.4505 


780 


608400 


474552000 


27.9285 


9.2052 


845 


714025 


603351125 


29.0689 


9.4541 


781 


609961 


476379541 


27.9464 


9.2091 


846 


715716 


605495736 


29.0861 


9.4578 


78*2 


611524 


478211768 


27.9643 


9.2130 


847 


717409 


607645423 


29.1033 


9.4615 


783 


613089 


480048687 


27.9821 


9.2170 


848 


719104 


609800192 


29.1204 


9.4652 


784 


614656 


4818^0104 


28. 


9.2209 


849 


720801 


611960049 


29.1376 


9.4690 


785 


616225 


483736625 


28.0179 


9.2248 


850 


722500 


614125000 


29.1548 


9.4727 


786 


617796 


485587656 


28.0357 


9.2287 


851 


724201 


616295051 


29.1719 


9.4764 


787 


619369 


487443403 


28.0535 


9.2326 


852 


725904 


618470208 


■29 1890 


9.4801 


788 


1S20944 


489303872 


28.0713 


9.2365 


853 


727609 


620650477 


29.2062 


9.4838 


7&y 


622521 


491169069 


28.0891 


9.2404 


854 


729316 


622835864 


29.22.33 


9.4875 


790 


624100 


493039000 


28.1069 


9.2443 


855 


731025 


625026375 


29.2404 


9.4912 


791 


625681 


494913671 


28.1247 


9.2482 


856 


732736 


627222016 


29.2575 


9.4949 


792 


627261 


4967;)3088 


28.1425 


9.2521 


857 


734449 


629422793 


29.2746 


9.4986 


793 


628849 


498677257 


28.1603 


9:2560 


858 


736164 


631628712 


29.2916 


9.5023 


794 


630436 


500566184 


28.1780 


9.2599 


859 


737881 


633839779 


29.3087 


9.5060 


795 


632025 


502459875 


28.1957 


9.2638 


860 


739600 


636056000 


29.3258 


9.5097 


796 


633616 


504358336 


28.2135 


9.2677 


861 


741321 


638277381 


29.3428 


9.5134 


797 


635209 


506261573 


28.2312 


9.2716 


862 


743044 


640503928 


29.3598 


9.5171 


798 


636804 


508169592 


28.2489 


9.2754 


863 


744769 


642785647 


29.3769 


9.520T 


799 


638401 


510082399 


28.2666 


9.2793 


864 


746496 


644972544 


29.3939 


9.5244 


800 , 


640000 


512000000 


28.2843 


9.2832 


865 


748225 


647214625 


29.4109 


9.5281 


801 


641601 


513922401 


28..3019 


9.2870 


866 


749956 


649461896 


29.4279 


9.5317 


802 


613204 


515849608 


28.3196 


9.2909 


867 


751689 


651714363 


29.4449 


9.5354 


803 


6U809 


517781627 


28.3373 


9.29-t8 


868 


. 753424 


653972032 


29.4618 


9.5391 


&0i 


646116 


519718464 


28.3549~ 


9.2986 


869 


755161 


656234909 


29.4788 


9.5427 


605 


64S025 


521660125 


28.3725 


9.3025 


870 


756900 


658503000 


29.4958 


9.5464 


80fi 


6196J6 


523606616 


28.3901 


9.3063 


871 


758641 


660776311 


29.5127 


9.5501 


807 


6512t9 


525557943 


28.4077 


9.3102 


872 


760384 


663054848 


29.5296 


9.553T 


808 


652864 


527514112 


28.4253 


9.3140 


873 


762129 


665338617 


29.5466 


9.5574 


809 


65U81 


529475129 


28.4429 


9.317» 


874 


763876 


667627624 


29.5635 


9.5610 


810 


656100 


531441000 


28.4605 


9.3217 


875 


765625 


669921875 


29.5804 


9.5647 


811 


657721 


533411731 


28.4781 


9.3255 


876 


767376 


672221376 


29.5973 


9.5683 


81-' 


KVMll 


535387328 


28.4956 


9.3294 


877 


769129 


674526133 


29.6142 


9.571» 


8!.i 


li ;o 111!) 


537367797 


28.5132 


9.3332 


878 


770884 


676836152 


29.6311 


9.5756 


gu 


«6Jo:-)o 


539353144 


28.5307 


9.3370 


879 


772641 


679151439 


29.6479 


9.5792 


815 


664225 


54134;«75 


28.5482 


9.3408 


880 


774400 


681472000 


29.6648 


9.5828 


616 


6f,5856 


543338496 


285657 


9..3447 


881 


776161 


683797841 


29.6816 


9.586& 


817 


H67489 


545338513 


28.5832 


9.3485 


882 


777924 


686128968 


29.6985 


9.5901 


8:& ' 


6.')!»124 


547313432] 


28.6007 


9.3523 


883 


779689 


688465387 


29.7153 


9.5937 


8i9 ■ 


670761 


5493532591 


28.6182 


9.3561 


884 


781456 


690807104 


29.7321 


9.5973 


b-JO 


672400 


551368000 


28.6356 


9.3599 


885 


783225 


693154125 


29.7489 


9.6010 


821 


674041 ! 


553387661 


28.6531 


9.3637 


886 


784996 


695506456 


29.7658 


9.6046 


822 


675684 


555412248 


28.6705 


9..3675 


887 


786769 


697864108 


29.7825 


9.6082 


823 


677329 


557441767 


28.6880 


9.3713 


888 


788544 


700227072 


29.7993 


9.6118 


824 


678976 


559476224 


28.7054 


9.3751 


889 


790321 


702595369 


29.8161 


9.6154 


825 


680625 


561515625 


28.7228 


9.3789 


890 


792100 


704969000 


29.8329 


9.6190 


826 


68J276 


563559976 


28.7402 


9.3827 


891 


793881 


707347971 


29.8496 


9.6226 


827 


683929 


565609283 


28.7576 


9.3865 


892 


795664 


709732288 


29.8664 


9.6262 


828 


685584 


567663552 


28.7750 


9..3902 


893 


797449 


712121957 


29.8831 


9.6298 


829 


687241 i 


569722789 


28.7924 


9.3940 


894 


799236 


714516984 


29.8998 


9.6334 


830 '< 


688900 1 


571787000 


28.8097 


9.3978 


895 


801025 


716917375 


29.9166 


9.6370 


asi 1 


690561 ' 


573856191 


28.8271 


9.4016 


896 


802816 


719323136 


29.9383 


9.6406 


832 i 


692224 


575930368 


28.8444 


9.4053 


897 


804609 


721734273 


29.9500 


9.6442 


833 


693889 


578009537 


28.8617 ! 


9.4091 


898 


806404 


724150792 


29.9666 


9.6477 


634 1 


695556 


580093704 


28.8791 1 


9.4129 


899 


808201 


726572699 


29.9833 


9.6513 


8»5 ' 


£97225 


582182875 


38.8964 1 


8.4166 


900 


810000 


729000000 


30. 


».<»4» 



TABLE NO. 75-CONCL. 193 

From Trantwine's <^'^ Civil Eng^ineer's Pocket Book.** 



SQUARES, CUBES, AND ROOTS. 

TABIiE of Squares, €nbes, Square Roots, and Cube Roots, 
of Numbers from 1 to 1000— (Continued.) 



No. 


Square. 


Cube. 


Sq. Bt. 


cut. 


No. 


Square. 


Cube. 


Sq. Rt. 


cut. 


901 


811801 


731432701 


30.0167 


9.6585 


951 


904401 


860085351 


30.8383 


9.833d 


902 


813604 


733870808 


30.0333 


9.6620 


952 


906304 


862801408 


30.8545 


9.8374 


903 


815409 


736314327 


30.0500 


9.6656 


953 


908209 


865523177 


30.8707 


9.8403 


904 


817216 


738763264 


30.0666 


9.6692 


954 


910116 


868250664 


80.8869 


9.8443 


905 


819025 


741217625 


30.0832 


9.6727 


955 


912025 


870983875 


30.9031 


9.8477 


906 


820836 


743677416 


30.0998 


9.6763 


956 


913936 


873J22816 


30.9192 


9.8511 


907 


822649 


746142643 


30.1164 


9.6799 


957 


915849 


876467493 


30.9354 


9.8546 


908 


824464 


748613312 


30.1330 


9.6834 


958 


917764 


879217912 


30.9516 


9.8580 


909 


826281 


751089429 


.30.1496 


9.6870 


959 


919681 


881974079 


30.9677 


9.8614 


910 


828100 


753571000 


30.1662 


9.6905 


960 


921600 


884736000 


30.9839 


9.8648 


911 


829921 


756058031 


30.1828 


9.6941 


961 


923521 


887503681 


31. 


9.8683 


912 


831744 


758550528 


30.1993 


9.6976 


962 


925444 


890277128 


31.0161 


9.8717 


913 


833569 


761048497 


30.2159 


9.7012 


963 


927369 


893056347 


31.0322 


9.8751 


914 


835396 


763551944 


30.2324 


9.7047 


964 


929296 


895841344 


31.0483 


9.8785 


915 


837225 


766060875 


30.2490 


9.7082 


965 


931225 


898632125 


31.0644 


9.8819 


916 


839056 


768575296 


30.2655 


9.7118 


966 


9.33156 


901428696 


31.0805 


9.8854 


917 


840889 


771095213 


30.2820 


9.7153 


967 


935089 


904231063 


31.0966 


9.8S88 


91>s 


842724 


773620632 


30.2985 


9.7188 


968 


937024 


907039232 


31.1127 


9.8922 


919 


844561 


776151559 


30.3150 


9.7224 


969 


938961 


909853209 


31.1288 


9.8956 


920 


846400 


778688000 


30.3315 


9.7259 


970 


940900 


912673000 


31.1448 


9.8990 


921 


848241 


781229961 


30..3480 


9.7294 


971 


942841 


915498611 


31.1609 


9.9024 


922 


850084 


783777448 


30.3645 


9.7329 


972 


944784 


918330048 


31.1769 


9.9058 


923 


851929 


786330467 


30.3809 


9.7364 


973 


946729 


921167317 


31.1929 


9.9092 


924 


853776 


788889024 


30.3974 


9.7400 


974 


948676 


924010424 


31.2090 


9.9126 


925 


855625 


791453125 


30.4138 


9.7435 


975 


950625 


926859375 


31.2250 


9.9160 


926 


857476 


794022776 


30.4302 


9.7470 


976 


952576 


929714176 


31.2410 


9.9194 


927 


859329 


796597983 


30.4467 


9.7505 


977 


954529 


932574833 


31.2570 


9.9227 


928 


861184 


799178752 


30.4631 


9.7540 


978 


956484 


935441352 


31.2730 


9.9261 


929 


863041 


801765089 


30.4795 


9.7575 


979 


958441 


938313739 


31.2890 


9.9295 


930 


864900 


804357000 


30.4959 


9.7610 


980 


960400 


941192000 


31.3050 


9.9329 


931 


866761 


806954491 


30.5123 


9.7645 


981 


962361 


944076141 


31.3209 


9.9363 


932 


868624 


809557568 


30.5287 


9.7680 


982 


964324 


946966168 


31.3369 


9.9396 


933 


870489 


812166237 


30.5450 


9.7715 


983 


966289 


949862087 


31.3528 


9.9430 


934 


872356 


814780504 


30.5614 


9.7750 


984 


968256 


952763904 


31.3688 


9.9464 


935 


874225 


817400375 


30.5778 


9.7785 


985 


970225 


955671625 


31.3847 


9.9497 


936 


876096 


820025856 


.30.5941 


9.7819 


986 


972196 


958585256 


31.4006 


9.9531 


937 


877969 


822656953 


30.6105 


9.7854 


987 


974169 


961504803 


31.4166 


9.9565 


938 


879844 


825293672 


30.6268 


9.7889 


988 


976144 


964430272 


31.4325 


9.9598 


939 


881721 


827936019 


30.6431 


9.7924 


989 


978121 


967361669 


31.4484 


9.9632 


940 


883600 


830584000 


30.6594 


9.7959 


990 


980100 


970299000 


31.4643 


9.9666 


941 


885481 


833237621 


30.6757 


9.7993 


991 


982081 


973242271 


31.4802 


9.9699 


942 


887364 


835896888 


30.6920 


9.8028 


992 


984064 


976191488 


31.4960 


9.9733 


943 


883249 


838561807 


30.7083 


9.8063 


993 


986049 


979146657 


31.5119 


9.9766 


944 


891136 


841232384 


30.7246 


9.8097 


994 


988036 


982107784 


31.5278 


9.980O 


945 


893025 


843908625 


30.7409 


9.8132 


995 


990025 


985074875 


31.5436 


9.9833 


946 


894916 


846590536 


30.7571 


9.8167 


996 


99-2016 


988047936 


31.5595 


9.9866 


947 


896809 


849278123 


30.7734 


9.8201 


997 


994009 


991026973 


31.5753 


9.9900 


948 


898704 


851971392 


30.7896 


9.8236 


998 


996004 


994011992 


31.5911 


9.9933 


949 


900601 


854670349 


.30.8058 


9.8270 


999 


998001 


997002999 


31.6070 


9.9967 


950 


902500 


857375000 


30.8221 


9.8305 


1000 


1000000 


1000000000 


31.6228 


10. 



To find the square or cube of any whole number ending: 
^vitli ciphers. First, omit all the final ciphers. Take from the table the 
square or cube (as the case may be) of the rest of the number. To this square add twice as many 
ciphers as there were final ciphers in the original number. To the cube add three times as many as 
in the original number. Thus, for 905002; 9052 — 819025. Add twice 2 ciphers, obtaining 8190250000. 
For 905003, 9053 = 741217625. Add i times 2 ciphers., obtaiiiiag 741217625000000. 



194 TABLE NO. 76. 

From Trautwine*s "Civil Eiig^iiieer's Pocket Book." 



SQUARE AND CUBE ROOTS. 



Square Roots and Cube Roots of Numbers from 1000 to 10000. 

No errors. 



Num. 


Sq. Rt. 


Cu. Rt. 


Xuni. 


Sq. Rt. 


Cu.Rt. 


Xum. 


Sq. Rt. 


Cu. Rt. 


Num, 


Sq. Rt. 


Cu. Rt. 


1005 


31.70 


10.02 


1405 


37.48 


11.20 


1805 


42.49 


12.18 


2205 


46.96 


13.02 


1010 


31.78 


10.03 


1410 


37.55 


11.21 


1810 


42.54 


12.19 


2210 


47.01 


13.03 


1015 


31.86 


10.05 


1415 


37.62 


11.23 


1815 


42.60 


12.20 


2215 


47.06 


13.04 


1020 


31.94 


10.07 


1420 


37.68 


11.24 


1820 


42.06 


12.21 


2220 


47.12 


13.05 


1025 


32.02 


10.08 


1425 


37.75 


11.25 


1825 


42.72 


12.22 


2225 


47.17 


13.05 


1030 


32.0iJ 


10.10 


14S0 


37.82 


11.27 


1830 


42.78 


12.23 


2230 


47.22 


13.06 


1035 


32.17 


10.12 


1435 


37.88 


11.28 


1835 


42.84 


12.24 


2235 


47.28 


13.07 


1040 


32.25 


10.13 


1440 


37.95 


11.29 


1840 


42.90 


12.25 


2240 


47.33 


13.08 


1045 


32.33 


10.15 


1445 


38.01 


11.31 


1845 


42.95 


12.26 


2245 


47.38 


13.09 


1050 


32.40 


10.10 


1450 


38.08 


11.32 


1850 


43.01 


12.-28 


2250 


47.43 


13.10 


1055 


32.48 


10.18 


1455 


38.14 


11.33 


1855 


43.07 


12.19 


2255 


47.49 


13.11 


1060 


32.56 


10.20 


1460 


38.21 


11.34 


1860 


43.13 


12.30 


2260 


47.54 


13.12 


1065 


32.63 


10.21 


1465 


38.28 


11.36 


1865 


43.19 


12.31 


22G5 


47. C9 


13.13 


1070 


32.71 


10.23 


1470 


38.34 


11.37 


1870 


43.24 


12.32 


2270 


47.64 


13.14 


1075 


32.79 


10.24 


1475 


38.41 


11.38 


1875 


43.30 


12.33 


2275 


47.70 


13.15 


1080 


32.86 


10.26 


1480 


38.47 


11.40 


1880 


43.36 


12.34 


22fc0 


47.75 


13.16 


1085 


32.94 


10.28 


1485 


38.54 


11.41 


1885 


43.42 


12.35 


2285 


47.80 


13.17 


1090 


33.02 


10.29 


1490 


38.C0 


11.42 


1800 


43.47 


12.36 


22<;0 


47.85 


13.18 


1095 


33.09 


10.31 


1495 


.38.07 


11.43 


1895 


43.53 


12.37 


2295 


47.91 


13.19 


1100 


33.17 


10.32 


1500 


38.73 


11.45 


1900 


43.59 


12.39 


2300 


47.96 


13.20 


1305 


33.24 


10.34 


1505 


38.79 


11.46 


1905 


43.65 


12.40 


2305 


48.01 


13.21 


1110 


33.32 


10.35 


1510 


38.86 


11.47 


1910 


43.70 


12.41 


2310 


48.06 


13.22 


1115 


33.39 


10.37 


1515 


38.92 


11.49 


1915 


43.76 


12.42 


2315 


48.11 


13.23 


1120 


33.47 


10.38 


1520 


38.!J9 


11.50 


1920 


43.82 


12.43 


2320 


48.17 


13.24 


1125 


33.54 


10.40 


1525 


39.05 


11.51 


1925 


43.87 


12.44 


2325 


48.22 


13.25 


1130 


33.62 


10.42 


1530 


39.12 


11.52 


1930 


43.93 


12.45 


2330 


48.27 


13.26 


1135 


33.69 


10.43 


1535 


39.18 


11.54 


1935 


43.99 


12.46 


2335 


48.32 


13.27 


1140 


33.76 


10.45 


1540 


39.24 


11.55 


1940 


44.05 


12.47 


2340 


48-37 


13.28 


1145 


33.84 


10.46 


1545 


39.31 


11.56 


1945 


44.10 


12.48 


2345 


48.43 


13.29 


1150 


33.91 


10.48 


1550 


39.37 


11.57 


1950 


44.16 


12.49 


2350 


48.48 


13.30 


1155 


33.99 


10.49 


1555 


39.43 


ll.c9 


1955 


44.22 


12.50 


2355 


48.53 


13.30 


1160 


34.06 


10.51 


1560 


39.50 


11. CO 


1960 


44.27 


12.51 


23C0 


48.58 


13.31 


1165 


34.13 


10.52 


1565 


39.56 


11.01 


i965 


44.33 


12.53 


2365 


48.63 


13.32 


1170 


34.21 


10.54 


1570 


39.02 


11.62 


1970 


44.38 


12.54 


2370 


48.68 


13.33 


1175 


34.28 


10.55 


1575 


39.69 


11.63 


1975 


44.44 


12.55 


2375 


48.73 


13.34 


1180 


34.35 


10.57 


1580 


39.75 


11.65 


1980 


44.50 


12.56 


2380 


48.79 


13.35 


1185 


34.42 


10.58 


1585 


39.81 


11.66 


1985 


44.55 


12.57 


2385 


48.84 


13.36 


1190 


34.50 


10.60 


1590 


39.87 


11.67 


1990 


44.61 


12.58 


2390 


48.89 


13.37 


1195 


34.57 


10.61 


1595 


39.94 


11.68 


1995 


44.67 


12.59 


2395 


48.94 


13.38 


1200 


34.64 


10.63 


1600 


40.00 


11.70 


2000 


44.72, 


12.60 


2400 


48.99 


13.39 


1205 


34.71 


10.64 


1605 


40.06 


11.71 


2005 


44.78 


12.61 


2405 


49.04 


13.40 


1210 


34.79 


10.66 


1610 


40.12 


11.72 


2010 


44.83 


12.62 


2410 


49.09 


13.41 


1215 


34.86 


10.67 


1615 


40.19 


11.73 


2015 


44.89 


12.63 


2415 


49.14 


13.42 


1220 


34.93 


10.69 


1620 


40.25 


11.74 


2020 


44.94 


12.64 


2420 


49.19 


13.43 


1225 


35.00 


10.70 


1625 


40.31 


11.76 


2025 


45.00 


12.65 


2425 


49.24 


13.43 


1230 


35.07 


10.71 


1630 


40.37 


11.77 


2030 


45.06 


12.66 


2430 


49.30 


13.44 


1235 


35.14 


10.73 


1635 


40.44 


11.78 


2035 


45.11 


12.67 


2435 


49.35 


13.45 


1240 


35.21 


10.74 


1640 


40.50 


11.79 


2040 


45.17 


12.68 


2440 


49.40 


13.46 


1245 


35.28 


10.76 


1645 


40.56 


11.80 


2045 


45.22 


12.69 


2445 


49.45 


13.47 


1250 


35.36 


10.77 


1650 


40.62 


11.82 


2050 


45.28 


12.70 


2450 


49.50 


13.48 


1255 


35.43 


10.79 


1655 


40.68 


11.83 


2055 


45.33 


12.71 


2460 


49.60 


13.50 


1260 


35.50 


10.80 


1660 


40.74 


11.84 


2060 


45.39 


12.72 


2470 


49.70 


13.52 


1265 


35.57 


10.82 


1665 


40.80 


11.85 


2065 


45.44 


12.73 


2480 


49.80 


13.54 


1270 


35.64 


10.83 


1670 


40.87 


11.86 


2070 


45.50 


12.74 


2490 


49.90 


13.55 


1275 


35.71 


10.84 


1675 


40.93 


11.88 


2075 


45.55 


12.75 


2500 


50.00 


13.57 


1280 


35.78 


10.86 


1680 


40.99 


11.89 


2080 


45 61 


12.77 


2510 


50.10 


13.59 


1285 


35.85 


10.87 


1685 


41.05 


11.90 


2085 


45.66 


12.78 


2520 


50.20 


13.61 


1290 


35.92 


10.89 


1690 


41.11 


11.91 


2090 


45.72 


12.79 


2530 


50.30 


13.63 


1295 


35.99 


10.90 


1695 


41.17 


11.92 


2095 


45.77 


12.80 


2540 


50.40 


13.64 


1300 


36.06 


10.91 


1700 


41.23 


11.93 


2100 


45.83 


12.81 


2550 


50 50 


13.66 


1305 


36.12 


10.93 


1705 


41.29 


11.95 


2105 


45.88 


12.82 


2560 


50,60 


13.68 


1310 


36.19 


10.94 


1710 


41.35 


11.96 


2110 


45.93 


12.83 


2570 


50.70 


13.70 


1315 


S6.26 


10.96 


1715 


41.41 


11.97 


2115 


45.99 


12.84 


2580 


50.79 


13.72 


1320 


86.33 


10.97 


1720 


41.47 


11.98 


2120 


46.04 


12.85 


2590 


50.89 


13.73 


1336 


36.40 


10.98 


1725 


41.53 


11.99 


2125 


46.10 


12.86 


2600 


50.99 


13.75 


1330 


36.47 


11.00 


1730 


41.59 


12.00 


2130 


46.15 


12.87 


2610 


51.09 


13.77 


1335 


36.54 


11.01 


1735 


41.65 


12.02 


2135 


46.21 


12.88 


2620 


51.19 


13.79 


1340 


36.61 


11.02 


1740 


41.71 


12.03 


2140 


46.26 


12.89 


2630 


51.28 


13.80 


1345 


36.67 


11.04 


1745 


41.77 


12.04 


2145 


46.31 


12.90 


2640 


51.38 


13.82 


1350 


36.74 


11.05 


1750 


41.83 


12.05 


2150 


46.37 


12.91 


2650 


51.48 


13.84 


1355 


36.81 


11.07 


1755 


41.89 


12.06 


2155 


46.42 


12.92 


2660 


51.58 


13.86 


1360 


36.88 


11.08 


1760 


41.95 


12.07 


2160 


46.48 


12.93 


2670 


51.67 


13. 8T 


1365 


36.95 


11.09 


1765 


42.01 


12.09 


2165 


46.53 


12.94 


2680 


51.77 


13.89 


1370 


37.01 


11.11 


1770 


42.07 


12.10 


2170 


46.58 


12.95 


2690 


51.87 


13.91 


1375 


37.08 


11.12 


1775 


42.13 


12.11 


2175 


46.64 


12.96 


2700 


51.96 


13.92 


1380 


37.15 


11.13 


1780 


42.19 


12.12 


2180 


46.69 


12.97 


2710 


52.06 


13.94 


1385 


37.22 


11.15 


1785 


42.25 


12.13 


2185 


46.74 


12.98 


2720 


52.15 


13.96 


1390 


37.28 


11.16 


1790 


42.31 


12.14 


2190 


46.80 


12.99 


27.30 


52.25 


13.98 


1395 


87.35 


11.17 


1795 


42.37 


12.15 


2195 


46.85 


13.00 


2740 


52.35 


13.99 


IMO 


37.42 


11.19 


1800 


42.43 


12.16 


2200 


46.90 


13.01 


2750 


52.44 


14,01 



TABLE NO. 76^0N^^^^^^T5d 
From Trautwine's ** Civil Eng^ineer's Pocket Book.'' 



SQUARE AND CUBE ROOTS. 



Square Roots and Cube Roots of Numbers from 1000 to 10000 

—(Continued.) 



Num. 


Sq. Rt. 


Cu. Rt. 


Num. 
3550 


Sq. Rt. 


Cu. Rt. 


Num. 


Sq. Rt. 


Cu.Rt. 


Num. 


Sq. Rt. 


Cu. Rt. 


2760 


52.54 


14.03 


59.58 


15.25 


4340 


65.88 


16.31 


5130 


71.62 


17.25 


2770 


52.63 


14.04 


3560 


59.67 


15.27 


4350 


65.95 


16.32 


5140 


71.69 


17.26 


2780 


52.73 


14.06 


3570 


59.75 


15.28 


4360 


66.03 


16.34 


5150 


71.76 


17.27 


2790 


52.82 


14.08 


3580 


59.83 


15.30 


4370 


66.11 


16.35 


5160 


71.83 


17.28 


2800 


52.92 


14.09 


3590 


59.92 


15.31 


4380 


66.18 


16.36 


5170 


71.90 


17.29 


2810 


53.01 


14.11 


3600 


60.00 


15.33 


4390 


66.26 


16.37 


5180 


71.97 


17.30 


2820 


53.10 


14.13 


3610 


60.08 


15.34 


4400 


66.33 


16.39 


5190 


72.04 


17.31 


2a30 


53.20 


14.11 


3620 


60.17 


15.35 


4410 


66.41 


16.40 


5200 


72.11 


17.32 


2810 


53.29 


14.16 


3630 


60.25 


15.37 


4420 


66.18 


16.41 


5210 


72.18 


17.34 


2850 


53.39 


14.18 


3610 


60.33 


15.38 


4130 


66.56 


16 12 


5220 


72.25 


17.35 


2860 


53.48 


14.19 


3650 


60.42 


15.40 


4440 


66.63 


16.11 


5230 


72.32 


17. .36 


2870 


53.57 


14.21 


3660 


60.50 


15.41 


4450 


66.71 


16.45 


5240 


72.39 


17.37 


2880 


53.67 


14.23 


3670 


60.58 


15.42 


4460 


66.78 


16.16 


5250 


72.46 


17.38 


2890 


53.76 


14.24 


3680 


60.66 


15.44 


4470 


6686 


16.47 


5260 


72.53 


17.39 


2900 


53.85 


14.26 


3690 


60.75 


15.45 


4180 


66.93 


16.49 


5270 


72.59 


17.40 


2910 


53.94 


14.28 


3700 


CO. 83 


15.47 


4490 


67.01 


16 50 


5280 


72.66 


17.41 


•2920 


54.04 


11.29 


3710 


60.91 


15.48 


4500 


67.08 


16.51 


5290 


72.73 


17.42 


2930 


54.13 


14.31 


3720 


60.99 


15.49 


4510 


67.16 


16.52 


5300 


72.80 


17.44 


2940 


54.22 


14. .33 


3730 


61.07 


15.51 


4520 


67.23 


16.53 


5310 


72.87 


17.45 


2950 


54.31 


14.34 


3740 


61.16 


15.52 


45.30 


67.31 


16.55 


5320 


72.94 


17.46 


2960 


54.41 


14.36 


3750 


61.24 


15.54 


4510 


67..38 


16.56 


5330 


73.01 


17.47 


2970 


54.50 


14.37 


3760 


61.32 


15.55 


4550 


67.45 


16.57 


•5340 


73.08 


17.48 


2980 


54.59 


14.39 


3770 


61.40 


15.56 


4560 


67.53 


16.58 


5350 


73.14 


17.49 


2990 


54.68 


14.41 


3780 


61.48 


15.58 


4570 


67.60 


16.59 


5360 


73.21 


17.50 


3000 


54.77 


14.42 


3790 


61.56 


15.59 


4580 


67.68 


16.61 


5370 


73.28 


17.51 


3010 


51.86 


14.44 


3800 


61 64 


15.60 


4590 


67.75 


16.62 


5380 


73.35 


17.52 


3020 


54.95 


11.45 


3810 


61.73 


15.62 


4600 


67. b2 


16.63 


5390 


73.42 


17.53 


3030 


55.05 


14.47 


3820 


61.81 


15.63 


4610 


67.S0 


16.64 


5400 


73.48 


17.54 


3010 


55.14 


14.49 


3630 


61.89 


15.65 


4620 


67.97 


16.C6 


5410 


73.55 


17.55 


3050 


55.23 


14.50 


3840 


61.97 


15.66 


4630 


68.04 


16.(i7 


5420 


73.62 


17.57 


3060 


55.32 


14.52 


3850 


62.05 


15.67 


4640 


68.12 


16.68 


5430 


73.69 


17.58 


3070 


55.41 


14.53 


3860 


62.13 


15.69 


4650 


68.19 


16.e9 


5440 


73.76 


17.59 


3080 


55.50 


14.55 


3870 


62.21 


15.70 


4660 


68.26 


16.70 


5450 


73.82 


17.60 


3090 


55.59 


14.57 


.3880 


62.29 


15.71 


4670 


68.34 


16.71 


5460 


73.89 


17.61 


3100 


55.68 


14.58 


3890 


62..37 


15.73 


4680 


68.41 


16.73 


5470 


73.96 


17.62 


3110 


55.77 


14.60 


3900 


62.45 


15.74 


4690 


68.18 


16.74 


5480 


74.03 


17.63 


3120 


55.86 


14.61 


3910 


62.53 


15.75 


4700 


6856 


16.75 


5490 


74.09 


17.64 


3130 


55.95 


14.63 


3920 


62.61 


15.77 


4710 


68.63 


16.76 


5500 


74.16 


17.65 


3110 


56.04 


14.64 


3930 


62.69 


15.78 


4720 


68.70 


16.77 


5510 


74.23 


17.66 


3150 


56.12 


14.66 


3940 


62.77 


15.79 


4730 


68.77 


16.79 


5520 


74.30 


17.67 


3160 


56.21 


14.67 


3950 


62.85 


15.81 


4740 


68.85 


16.80 


5530 


74.36 


17.68 


3170 


56.30 


14.69 


3960 


62.93 


15.82 


4750 


68.92 


16.81 


5540 


74.43 


17.69 


3180 


56.39 


14.71 


3970 


63.01 


15.83 


4760 


68.99 


16.82 


5550 


74.50 


17.71 


3199 


56.48 


14.72 


3980 


63.09 


15.85 


4770 


69.07 


16.83 


5560 


74.57 


17.72 


3200 


56.57 


14.74 


3990 


63.17 


15.86 


4780 


69.14 


16.85 


5570 


74.63 


17.73 


3210 


56,66 


14.75 


4000 


63.25 


15.87 


4790 


69.21 


16.86 


5580 


74.70 


17.74 


3220 


56.75 


14.77 


4010 


63.32 


15.89 


4800 


69.28 


16.87 


5590 


74.77 


17.75 


3230 


56.83 


14.78 


4020 


63.40 


15.90 


4810 


69.35 


16.88 


5600 


74.83 


17.76 


3240 


56.92 


14.80 


4030 


63.48 


15.91 


4820 


69.43 


16 89 


5610 


74.90 


17.77 


3250 


57.01 


14.81 


4040 


63.56 


15.93 


4830 


69.50 


16.90 


5620 


74.97 


17.78 


3260 


57.10 


14.83 


4050 


63.64 


15.94 


4840 


69.57 


16.92 


5630 


75.03 


17.79 


3270 


57.18 


14.84 


4060 


63.72 


15.95 


4850 


69.64 


16.93 


5640 


75.10 


17.89 


3280 


57.27 


14.86 


4070 


63.80 


15.97 


4860 


69.71 


16.94 


5650 


75.17 


17.81 


3290 


57.36 


14.87 


4080 


63.87 


15.98 


4870 


69.79 


16.95 


5660 


75.23 


17.82 


3300 


57.45 


14.89 


4090 


63.95 


15.99 


4880 


69.86 


16.96 


5670 


75.30 


17.83 


3310 


57.53 


14.90 


4100 


64.03 


16.01 


4890 


69.93 


16.97 


5680 


75.37 


17.84 


3320 


57.62 


14.92 


4110 


64.11 


16.02 


4900 


70.00 


16.98 


5690 


75.43 


17.85 


3330 


57.71 


14.93 


4120 


64.19 


16.03 


4910 


70.07 


17.00 


5700 


75.50 


17.86 


3340 


57.79 


14.95 


4130 


64.27 


16.04 


4920 


70.14 


17.01 


5710 


75.56 


17.87 


3350 


57.88 


14.96 


4140 


64.34 


16.06 


4930 


70.21 


17.02 


5720 


75.63 


17.88 


3360 


57.97 


14.98 


4150 


64.42 


16.07 


4940 


70.29 


17.03 


5730 


75.70 


17.89 


3370 


58.05 


14.99 


4160 


64.50 


16.08 


4950 


70.36 


17.04 


5740 


75.76 


17.90 


3380 


58.14 


15,01 


4170 


64.58 


16.10 


4960 


70.43 


17.05 


5750 


75.83 


17.92 


3390 


58.22 


15.02 


4180 


64.65 


16.11 


4970 


70.50 


17.07 


5760 


75.89 


17.93 


3400 


58.31 


15.04 


4190 


64.73 


16.12 


4980 


70.57 


17.08 


5770 


75.96 


17.94 


3410 


58.40 


15.05 


4200 


64.81 


16.13 


4990 


70.64 


17.09 


5780 


76.03 


17.95 


3420 


58.48 


15.07 


4210 


64.88 


16.15 


5000 


70.71 


17.10 


5790 


76.09 


17.96 


3430 


58.57 


15.08 


4220 


64.96 


16.16 


5010 


70.78 


17.11 


5800 


76.16 


17.97 


3440 


58.65 


15.10 


4230 


65.04 


16.17 


5020 


70.85 


17.12 


5810 


76.22 


17.98 


3450 


58.74 


15.11 


4240 


65.12 


16.19 


5030 


70.92 


17.13 


5820 


76.29 


17.99 


3460 


58.82 


15.12 


feo 


65.19 


16.20 


5040 


70.99 


17.15 


5a30 


76.35 


18.00 


3470 


58.91 


15.14 


4260 


65.27 


16.21 


5050 


71.06 


17.16 


5840 


76.42 


18.01 


3480 


58.99 


15.15 


4270 


65.35 


16.22 


5060 


71.13 


17.17 


5850 


76.49 


18.02 


"3490 


59.08 


15.17 


4280 


65.42 


16.24 


5070 


71.20 


17.18 


5860 


76.55 


18.03 


3500 


59.16 


15.18 


4290 


65.50 


16.25 


5080 


71.27 


17.19 


5870 


76.62 


18.04 


3510 


59.25 


15.20 


4300 


65 57 


16.26 


5090 


71.34 


17.20 


5880 


76.68 


18.05 


3520 


59.33 


15.21 


4310 


65.65 


16.27 


5100 


71.41 


17.21 


5890 


76.75 


18.06 


3530 


59.41 


15.23 


4320 


65.73 


16.29 


5110 


71.48 


17.22 


5900 


76.81 


18.07 


35M 


59.50 


15.24 


4330 


65.80 


16.30 


5120 


71.55 1 


17.24 


5910 


76.88 


18.03 



^ 



m— 'CUA- 



From Trautwine's *' Civil Engineer's Pocket Book.- 



SQUARE AND CUBE ROOTS. 



Square Roots and Cube Roots of ^Tumbers from 1000 to 10000 

— (Continued.) 



Num. 


Sq. Rt. 


Cu. Rt. 


Num. 


Sq. Rt. 


jCu.Rt. 


Num. 


Sq. Rt. 


Cu. Rt. 


Num. 


Sq. Rt. 


[ Cu. Rt 


6920 


76.94 


18.09 


6710 


81.91 


18.86 


7500 


86.60 


19.57 


8290 


91.05 


20.24 


593e 


77.01 


18.10 


6720 


81.98 


18.87 


7510 


86.66 


19.58 


8300 


91.10 


20.25 


5940 


77.07 


18.11 


6730 


82.04 


18.88 


7520 


86.72 


19.59 


8310 


91.16 


20.26 


5950 


77.14 


18.12 


6740 


82.10 


18.89 


7530 


86.78 


19.60 


8320 


91.21 


20.26 


5960 


77.20 


18.13 


6750 


82.16 


18.90 


7540 


86.83 


19.61 


8330 


91.27 


20.27 


5970 


77.27 


18.14 


6760 


82.22 


18.91 


7550 


86.89 


19.62 


8340 


91.32 


20.28 


5980 


77.33 


18.15 


6770 


82.28 


18.92 


7560 


86.95 


19.63 


8350 


91.38 


20.29 


6990 


77.40 


18.16 


6780 


82.34 


18.93 


7570 


87.01 


19.64 


8360 


91.43 


20.30 


6000 


77.46 


18.17 


6790 


82.40 


18.94 


7580 


87.06 


19.64 


8370 


91.49 


20.30 


6010 


77.52 


18.18 


6800 


82.46 


18.95 


7590 


87.12 


19.65 


8380 


91.54 


20.31 


6020 


77.59 


18.19 


6810 


82.52 


18.95 


7600 


87.18 


19.66 


8390 


91.60 


20.32 


6030 


77.65 


18.20 


6820 


82.58 


18.96 


7610 


87.24 


19.67 


8400 


91.65 


20.33 


6040 


77.72 


18.21 


6830 


82.64 


18.97 


7620 


87.29 


19.68 


8410 


91.71 


20.34 


6050 


77.78 


18.22 


6840 


82.70 


18.98 


7630 


87.35 


19.69 


8420 


91.76 


20.34 


6060 


77.85 


18.23 


6850 


82.76 


18.99 


7640 


87.41 


19.70 


8430 


91.82 


20.35 


6070 


77.91 


18.24 


6860 


82.83 


19.00 


7650 


87.46 


19.70 


8440 


91.87 


20.36 


6080 


77.97 


18.25 


6870 


82.89 


19.01 


7660 


87.52 


19.71 


8450 


91.92 


20.37 


6090 


78.04 


18.26 


6880 


82.95 


19.02 


7670 


87.58 


19.72 


8460 


91.98 


20.38 


6100 


78.10 


18.27 


6890 


83.01 


19.03 


7680 


87.64 


19.73 


8470 


92.03 


20.38 


6110 


78.17 


18.28 


6900 


83.07 


19.04 


7690 


87.69 


19.74 


8480 


92.09 


20.39 


6120 


73.23 


18.29 


6910 


83.13 


19.05 


7700 


87.75 


19.75 


8490 


92.14 


20.40 


i6130 


78.29 


18..30' 


6920 


83.19 


19.06 


7710 


87.81 


19.76 


8500 


92.20 


20.41 


6140 


78.36 


18.31 


6930 


83.25 


19.07 


7720 


87.86 


19.76 


8510 


92.25 


20.42 


6150 


78.42 


18.32 


6940 


83.31 


19.07 


7730 


87.92 


19.77 


8520 


92.30 


20.42 


6160 


78.49 


18.33 


6950 


83.37 


19.08 


7740 


87.98 


19.78 


8530 


92.36 


20.43 


6170 


78.55 


18.34 


6960 


83.43 


19.09 


7750 


88.03 


19.79 


8540 


92.41 


20.44 


6180 


78.61 


18.35 


6970 


83.49 


19.10 


7760 


88.09 


19.80 


8550 


92.47 


20.45 


6190 


78.68 


18..S6 


6980 


83.55 


19.11 


7770 


88.15 


19.81 


8560 


92.52 


20.46 


6200 


78.74 


18.37 


6990 


83.61 


19.12 


7780 


88.20 


19.81 


8570 


92.57 


20.46 


6210 


78.80 


18.38 


7000 


83.67 


19.13 


7790 


88.26 


19.82 


8580 


92.63 


20.47 


6220 


"78.87 


18.39 


7010 


83.73 


19.14 


7800 


88.32 


19.83 


8590 


92.68 


20.48 


6230 


78.93 


18.40 


7020 


83.79 


19.15 


7810 


88.37 


19.84 


8600 


92.74 


20.49 


6240 


78.99 


18.41 


7030 


83.85 


19.16 


7820 


88.43 


19.85 


8610 


92.79 


20.50 


6250 


79.06 


18.42 


7040 


83. yo 


19.17 


7830 


88.49 


19.86 


8620 


92.84 


20.50 


6260 


79.12 


18.43 


7050 


83. so 


19.17 


7840 


88.54 


19.87 


8630 


92.90 


20.51 


6270 


79.18 


18.44 


7060 


84.02 


19.18 


7850 


88.60 


19.87 


8640 


92.95 


20.52 


6280 


79.25 


18.45 


7070 


84.08 


19.19 


7860 


88.66 


19.88 


8650 


93.01 


20.53 


6290 


79 31 


18.46 


7080 


84.14 


19.20 


7870 


88.71 


19.89 


8660 


93.06 


20.54 


6300 


79.37 


18.47 


7090 


84.20 


19.21 


7880 


88.77 


19.90 


8670 


93.11 


20.54 


6310 


79.44 


18.48 


7100 


84.26 


19.22 


7890 


88.83 


19.91 


8680 


93.17 


20.55 


6320 


79.50 


18.49 


7110 


84.32 


19.23 


7900 


88.88 


19.92 


8690 


93.22 


20.56 


6330 


79.56 


18.50 


7120 


84.. 38 


19.24 


7910 


88.94 


19.92 


8700 


93.27 


20.57 


6340 


79.62 


18.51 


7130 


84.44 


19.25 


7920 


88.99 


19.93 


8710 


93.33 


20.57 


6350 


79.69 


18.52 


7140 


84.50 


19.26 


7930 


89.05 


19.94 


8720 


93.38 


20.58 


6360 


79.75 


18.53 


7150 


84.56 


19.26 


7940 


89.11 


19.95 


8730 


93.43 


20.59 


6370 


79.81 


18.54 


7160 


84.62 


19.27 


7950 


89.16 


19.96 


8740 


93.49 


20.60 


6380 


79.87 


18.55 


7170 


84.68 


19.28 


7960 


89.22 


19.97 


8750 


93.54 


20.61 


6390 


79.94 


18.56 


7180 


84.73 


19.29 


7970 


89.27 


19.97 


8760 


93.59 


20.61 


6400 


80.00 


18.57 


7190 


84.79 


19.30 


7980 


89.33 


19.98 


8770 


93.65 


20.62 


6410 


80.06 


18.58 


7200 


84.85 


19.31 


7990 


89.39 


19.99 


8780 


93.70 


20.6S 


6420 


80.12 


18.59 


7210 


84.91 


19.32 


8000 


89.44 


20.00 


8790 


93.75 


20.64 


6430 


80.19 


18.60 


7220 


84.97 


19.33 


8010 


89.50 


20.01 


8800 


93.81 


20.65 


6440 


80.25 


18.60 


7230 


85.03 


19.34 


8020 


89.55 


20.02 


8810 


93.86 


20.65 


6450 


80.31 


18.61 


7240 


85.09 


19.35 


8030 


89.61 


20.02 


8820 


93.91 


20.66 


6460 


80.37 


18.62 


7250 


85.15 


19.35 


8040 


89.67 


20.03 


8830 


93.97 


20.67 


6470 


80.44 


18.63 


7260 


85.21 


19.36 


8050 


89.72 


20.04 


8840 


94.02 


20.68 


6480 


80.50 


18.64 


7270 


85.26 


19.37 


8060 


89.78 


20.05 


8850 


94.07 


20.68 


6490 


80.56 


18.65 


7280 


85.32 


19.38 


8070 


89.83 


20.06 


8860 


94.13 


20.6» 


6500 


80.62 


18.66 


7290 


85.38 


19.39 


8080 


89.89 


20.07 


8870 


94.18 


20. -a 


6510 


80.68 


18.67 


7300 


85.44 


19.40 


8090 


89.94 


20.07 


8880 


94.23 


20.71 


6520 


80.75 


18.68 


7310 


85.50 


19.41 


8100 


90.00 


20.08 


8890 


94.29 


20.72 


6530 , 


80.81 


18.69 


7320 


85.56 


19.42 


8110 


90.06 


20.09 


8900 


94.34 


20.72 


6540 


80.87 


18.70 


7330 


85.62 


19.43 


8120 


90.11 


20.10 


8910 


94.. 39 


20.75 


6550 


80.93 


18.71 


7340 


85.67 


19.43 


8130 i 


90.17 


20.11 


8920 


94.45 


20.74 


6560 


80.99 


18.72 


7350 


85.73 


19.44 


8140 


90.22 


20.12 


8930 


94.50 


20.75 


6570 


81.06 


18.73 


7360 


85.79 


19.45 


8150 


90.28 


20.12 


8940 


94.55 


20.75 


6580 ; 


81.12 


18.74 


7370 


85.85 


19.46 


8160 


90.33 


20.13 


8950 


94.60 


20.76 


6590 


81.18 


18.75 


7380 1 


85.91 


19.47 


8170 


90.39 i 


20.14 


8960 


94.66 


20.77 


660e , 


81.24 


18.76 


7390 


85.97 


19.48 


8180 


90.44 


20.15 


8970 


94.71 


20.78 


6610 t 


81.30 


18.77 


7400 I 


86.02 


19.49 


8190 


90.50 


20.16 


8980 


94.76 


20.79 


6620 1 


81.36 


18.78 


7410 1 


86.08 


19.50 


8200 ' 


90.55 


20.17 


8990 


94.82 


20.79 


6630 


81.42 


18.79 


7420 


86.14 


19.50 


8210 


90.61 , 


20.17 


9000 


94.87 


20.80 


6640 , 


81.49 


18.80 


7430 ' 


86.20 


19.51 


8220 


90.66 1 


20.18 


9010 


94.92 


20.81 


6650 j 


81.55 


18.81 


7440 


86.26 


19.52 


8230 


90.72 i 


20.19 


9020 


94.97 


20.82 


6660 1 


81.61 


18.81 


7450 


86.31 


19.53 


8240 


90.77 1 


20.20 


9030 


95.03 


20.62 


6670 i 


81.67 


18.K2 


7460 


86..37 


19.54 


8250 


90.83 


20.21 


9040 


95.08 


20.83 


6680 


81.73 


18.83 


7470 


86.43 


19.55 


8260 


90.88 


20.21 


905C 


95.13 


20.84 


6690 


81.79 


1«.H4 


7480 


86 49 


19.56 


8270 


90.94 


20.22 


9060 


95.18 


20.85 


6700 ' 


81.85 


l^.«5 


7490 


86.54 


19.57 


8280 


90.99 


20.23 


9070 


95.24 


20.8& 



TA13LE NO. 72— 0O]Sr. 197 

From Trautwine's "'Civil Kiijsineer's Pocket BooR." 

SQUARE AND CUBE ROOTS. 



Square Roots and Cube Roots of Numbers from 1000 to 10000 

— (Continued.) 



Num. 


Sq. Kt. 


Cu. Rt. 


\um. 


Sq. Rt. 


Cu. Rt. 


Num. 


Sq. Rt. 


Cu.Rt. 


\um. 


Sq. Rt. 


Cu. Rt. 


9080 


95.29 


20.86 


9320 


96.54 


21.04 


9550 


97.72 


21.22 


9780 


98.89 


21. .39 


9090 


95.34 


20.87 


9330 


96.59 


21.05 


9560 


97.78 


21.22 


9790 


98.94 


21.39 


9100 


95.39 


20.88 


9340 


96.64 


21.06 


9570 


97.83 


21.23 


9800 


98.99 


21.40 


9110 


95.45 


20.89 


9350 


96.70 


21.07 


9580 


97 88 


21.24 


9810 


99.05 


21.41 


9120 


95.50 


20.89 


9360 


96.75 


21.07 


9590 


97.93 


21.25 


9820 


99.10 


21.41 


9130 


95.55 


20.90 


9370 


96.80 


21.08 


9600 


97.98 


21.25 


9830 


99.15 


21.42 


9140 


96.60 


20.91 


9380 


96.85 


21.09 


9610 


98.03 


21.26 


9840 


99.20 


21.43 


9150 


95.66 


20.92 


9390 


96.90 


21.10 


9620 


98.08 


21.27 


9850 


99.25 


21.44 


9160 


95.71 


20.92 


9400 


96.95 


21.10 


9630 


98.13 


21.28 


9860 


99.30 


21.44 


91 TO 


95.76 


20.93 


9410 


97.01 


21.11 


9640 


98.18 


21.28 


9870 


99.35 


21.45 


9180 


95.81 


20.94 


9420 


97.06 


21.12 


9650 


98.23 


21.29 


9880 


99.40 


21.46 


9190 


95.86 


20.95 


9430 


97.11 


21.13 


9660 


98.29 


21.30 


9890 


99.45 


21.47 


9200 


95.92 


20.95 


9440 


97.16 


21.13 


9670 


98.34 


21.30 


9900 


99.50 


21.47 


9210 


95.97 


20.96 


9450 


97.21 


21.14 


9680 


98.39 


21.31 


9910 


99.55 


21.48 


9220 


96.02 


20.97 


9460 


97.26 


21.15 


9690 


98.44 


21.32 


9920 


99.60 


21.49 


9230 


96.07 


20.98 


9470 


97.31 


21.16 


9700 


98.49 


21.33 


9930 


99.65 


21.49 


9240 


96.12 


20.98 


9480 


9i.il 


21.16 


9710 


98.54 


21.33 


9940 


99.70 


21.50 


9250 


96.18 


20.99 


9490 


97.42 


21.17 


9720 


98.59 


21.34 


9950 


99.75 


21.51 


9260 


96.23 


21.00 


9500 


97.47 


21.18 


9730 


98.64 


21.35 


9960 


99.80 


21.52 


9270 


96.28 


21.01 


9510 


97.52 


21.19 


9740 


98.69 


21.36 


9970 


99.85 


21.52 


9280 


96.33 


21.01 


9520 


97.57 


21.19 


9750 


98.74 


21.36 


9980 


99.90 


21.53 


9290 


96.38 


21.02 


9530 


97.62 


21.20 


9760 


98.79 


21.37 


9990 


99.95 


21. 5i 


9300 


96.44 


21.03 


9540 


97.67 


21.21 


9770 


98.84 


21.38 


10000 


100.00 


21 .5i 


9310 


96.49 


21.04 





















To fin<l Square or €nbe Roots of larg-e numbers not con- 
tained in tlie column of numbers of tbe table. 

Such TOOLS may sometimes be taken at once from the table, by merely regarding the columns of 
powers as being columns of numbers; and those of numbers as being those of roots. Thus, if the 
tq rt of 25281 is reqd, first find that number in the column of squares: and opposite to it, in the 
column of numbers, is its sq rt 159. For the cube rt of 857375, find that number in the column of 
cu6e«; and opposite to it, in the col of numbers, is its cube rt 95. When the e.xact number is not con- 
tained in the column of squares, or cubes, as the case may be, we may use iastpnd the number nearest 
to it, if no great accuracy is reqd. But when a considerable degree of accuracy is necessary, the 
following very correct methods may be used. 

For the square root. 

This rule applies both to whole numbers, and to those which arepai'tly (not wholly) decimal- First, 
im the foregoing manner, take out the tabular number, which is nearest to the given one ; and also its 
tabular sq rt. Mult this tabular number by 3 ; to the prod add the given number. Call the sum A. 
Then mult the given number by 3; to the prod add the tabular number. Call the sum B. Then 

: Tabular root : Reqd root. 
Here we find the nearest tabular number to be 947 ; and Its 

r 946.53 = given num. 
3 



A : B : 

Ex. Let the given number be 946.53. 
tabular sq rt 30.7734. Hence, 

947 = tab num 
3 



2841 
946.53 =: giren num. 



3787.53 = A. 



and <i 2839.59 



I 947 =:tab 
I3786.59 = B. 



= tab num. 



A. 

3787.53 



B. 
3786.59 



Tab root. 
30.7734 ; 



Reqd root. 
Then 3787.53 : 3786.59 : : 30.7734 : 30.7657 -f-. 

The root as found by actual mathematical process is also 30.7657 -f-. 

For the cube root. 

This rule applies both to whole numbers, and to those which are partly decimal. First take out tne 
tabular number which is nearest to the given one ; and also its tabular cube rt. Mult this tabul.ar 
number by 2 ; and to the prod add the given number. Call the sum A. Then mult the given number 
by 2; and to the prod add the tabular number. Call the sum B. Then 

A : B : : Tabular root : Reqd root. 
Ex. Let the given number be 7.368. Here we find the nearest tabular number (in tbe column of 

Hence, 



tube*) to be 6859; and its tabular cube rt 19 
6859 == tab num 



1.3718 
7368 = given num. 1 

21086 = A. J 



1 i 

5- and -i 



7368 =r giv?n num. 
2 



14736 
6859 = tab num. 



L 21595 =: B. 



B. 
21595 



Tab Root. 
: 19 : 



Reqd Rt. 
19.4585 



Then, as 21086 

The root as found hy correct maihcw.tica\ process is 19.4588. 



The engineer rarely requires even 



198 
From Trantwine's '^ Civil Engineer's Pocket Book.'* 



SQUARE AND CUBE ROOTS. 

ttiis degree of accuracy; for his purposes, therefore, this process is greatly preferable to the ordinary 
laborious one. 

To find the square root of a number w^taich is wholly 

decimal. 

Very simple, and correct to the third numeral figure inclusive. If the number does not contain at 
least five figures, counting from the first numeral, Mid including it, add one or more ciphers to make 
five. If, after that, the whole number is not separable into twos, add another cipher to make it so. 
Then beginuing at the first numeral figure, and including it, assume the number to be a whole one. 
In the table find the number nearest to this assumed one ; take out its tabular sq rt ; move the deci- 
mal poiQt of this tabular root to the left, Italf a,s many places as the finally modified decimal number 
has figures. 

Ex. What is the sq rt of the decimal .002? Here, in order to have at least five decimal figures, 
counting from the first numeral (2). and including it, add ciphers thus, .00,20,00,0. But, as it is not 
now separable into twos, add another cipher, thus, .00,20,00,00. Then beginuing at the first numeral 
(«), assume this decimal to be the whole number 200000. The nearest to this in the table is 199809; 
and the sq rt of this is 447. Now, ihe decimal number as finally modified, namely, .00,20,00,00, has 
eight figures ; one- half of which is 4 ; therefore, move the decimal point of the root 447, four places to 
the left; making it .0447. This is the reqd sq rt of .002, correct to the third numeral 7 included. 

To find the cube root of a number w^hich is nrholly decimal. 

Very simple, and correct to the third numeral inclusive. 

If the number does uot contain at least five figures, counting from the first numeral, and including 
it, add one or more ciphers to make five. If, after that, the number is not separable into threes, add 
one or more ciphers to make it so. Then beginning at the first numeral, and including it, assume 
the number to be a whole one. In the table find the number nearest to this assumed one, and take 
out its tabular cub rt. Move the decimal point of this rt to the left, one-third as many places as the 
finally modified decimal number has figures. 

Ex. What is the cube rt of the decimal .002 ? Here, in order to have at least five figures, counting 
from the first numeral (2), and including it, add ciphers thus, .002,000,0. But as it is not now separ- 
able into threes, add two more ciphers to make it so ; thus, .002,000,000. Then beginning with the 
first numeral (2), assume the decimal to be the whole number 2000000. The nearest cube to this in 
the table in the column of cubes, is 2000376 ; and its tabular cube rt as found in the col of numbers, 
is 126. Now, the decimal number as finally modified, namely, .002 000 000, has nine figures ; one^third 
of which is 3 ; therefore, move the decimal point of the root 126, three places to the left, making it 
.126. Thia is the reqd cube rt of the decimal .002, correct to the third numeral 6 included. 

TO find roots by logarithms, | ^^^^^02! 
For tables of sq. rts. of 5th powers see table 69, page 166. 

To find the sq. or cu. rt. of a number consisting of intigers 
and decimals. 

Multiply the difference between the root of the intiger part of the given 
number, and the root of the next higher number, by the decimal part of 
the given number, and add the product to the root of the given intiger. 
The sum is the root required. 

Ex.— Required the sq. rt. of 20.321— square root of 21 = 4.5825 

" " 20 = 4.4721 

Difference = .1104 
.1104 X .321 = .354384. add to rt. of 20, 4.4721, and get 4.5075384=rt. required. 
Ex.— Required the cu. rt. of 16.42— cube root of 17 = 2.5712 

" " ^' 16 = 2.5198 

Difference = .0514 
.0514 X .42 = .021588, add to rt. of 16, 2.5198, and get 2.541388 = rt. required. 

To find the sq. or cu. rt. of a higher number than is contain- 
ed in the table, when the number is divisib'e by 4 or 8 with- 
out leaving a remainder. 

Rule.— Divide the number by 4 or 8 respectively, as the sq. or cu. rt. is re- 
quired ; take the rt. of the quotient in the table, multiply it by 2, 
and the product will be the root required. 
Ex.— What are the square and cube roots of 2400? 

2400 -^ 4 = 600 and 2400 -4- 8 = 300. 

Then the sq. rt. of 600, per table, = 24.4949, which, being X 2 = 48.9898 = 
sq. rt. required. 

Then the cu. rt. of 300, per table, = 6.6943, which, being X 2 = 13.3886 = 
cu. rt. required. 

To find the 4th root of any number. 
Take the square root of its square root. 

To find the 6th root of any number. 

Take the cube root of its square root. 

To find any root or any power by logarithms see pages 200 and 202. 



TABLE NO. 77. 
I^o^ari thins of lumbers, from O to 1000.* 



190 



No. 





■ 1 


2 


3 4 


5 


6 


■ 7 


8 


9 


Prop. 








00000 


30103 


47712 


60206 


69897 


77815 


84510 90309 


95424 




10 


00000 


00432 


00860 


01283 


01703 


02118 


02530 


02938 


. 03342 


03742 


415 


11 


04139 


04532 


04921 


05307 


05690 


06069 


06445 


06818 


07188 


07554 


379 


12 


07918 


08278 


08636 


08990 


09342 


09691 


10037 


10380 


10721 


11059 


349 


13 


11394 


11727 


12057 


12385112710 


1.3033 


13353 


13672 


13987 


14301 


323 


14 


14613 


14921 


15228 


15533:15836 


16136 


16435 


16731' 17026 


17318 


300 


15 


17609 


17897 


18184 


18469 


18752 


19033 


19.312 


19590 19865 


20139 


281 


16 


20412 


20682 


20951 


21218 


21484 


21748 


22010 


22271 


22530 


22788 


264 


17 


23045 


23299 


23552 


23804 


24054 


24303 


24551 


24797 


25042 


25285 


249 


18 


25527 


25767 


26007 


26245 


26481 


26717 


26951 


27184 


27415 


27646 


236 


19 


27875 


28103 


28330 


28555 


28780 


29003 


29225 


29446 


29666 


29885 


223 


20 


30103 


30319 


30535 


30749 


30963 


31175 


31386 


31597 


31806 


32014 


212 


21 


32222 


32428 


32633 


32838 


33041 


33243 


33445 


33646 


33845 


34044 


202 


22 


34242 


3W39 


34635 


34830 


35024 


35218 


35410 


35602 


35793 


35983 


194 


23 


36173 


36361 


36548 


36735 


36921 


37106 


37291 


37474 


37657 


37839 


185 


•24 


38021 


38201 


38381 


38560 


38739 


38916 


39093 


39269 


39445 


39619 


177 


25 


39794 


39967 


40140 


40312 


40483 


40654 


40824 


40993 


41162 


41330 


171 


26 


41497 


41664 


41830 


41995 


42160 


42324 


424SS 


42651 


42813 


42975 


164 


27 


43136 


43296 


43156 


43616 


43775 


43933 


44090 


44248 


44404 


44560 


158 


28 


44716 


44870 


45024 


45178 


45331 


45484 


45636 


45788 


45939 


46089 


153 


29 


46240 


46389 


46538 


46686 


46834 


46982 


47129 


47275 


47421 


47567 


148 


30 


47712 


47856 


48000 


48144 


48287 


48430 


48572 


48713 


48856 


48995 


143 


31 


49136 


49276 


49415 


49554 


49693 


49831 


49968 


50105 


50242 


50379 


138 


32 


50515 


50650 


50785 


50920 


51054 


51188 


51321 


51454 


51587 


51719 


134 


33 


51851 


51982 


52113 


52244 


52374 


52504 


52633 


52763 


52891 


53020 


130 


34 


53148 


53275 


53402 


53529 


53655 


53781 


53907 


54033 


54157 


54282 


126 


35 


54407 


54530 


54654 


54777 


54900 


55022 


55145 


55266 


55388 


55509 


122 


36 


55630 


55750 


55870 


55990 


56110 


56229 


56348 


56466 


56584 


56702 


119 


37 


56820 


56937 57054 


57170 


57287 


57403 


57518 


57634 


57749 


57863 


116 


38 


57978 


58092 58206 


58319 


58433 


58546 


58658 


58771 


58883 


58995 


113 


39 


59106 


59217 59328 


59439 


59549 


59659 


59769 


59879 


59988 


60097 


110 


40 


60206 


60314 1 60422 


60530 


60638 


60745 


60852 


60959 


61066 


61172 


107 


41 


61278 


61384 61489 


61595 


61700 


61804 


61909 


62013 


62118 


62221 


104 


42 


62325 


62428 62531 


62634 


62736 


62838 


62941 


63042 


63144 


63245 


102 


43 


63347 


63447 


63548 


63648 


63749 


63848 


63948 


64048 


64147 


64246 


99 


44 


64345 


64443 


64542 


64640 


64738 


64836 


64933 


65030 


65127 


65224 


98 


45 


65.321 


65417 


65513 


65609 


65705 


65801 


65896 


65991 


66086 


66181 


96 


46 


66276 


66370 


66464 


66558 


66651 


66745 


66838 


66931 


67024 


67117 


94 


47 


67210 


67.302 


67394 


67486 


67577 


67669 


67760 


67851 


67942 


68033 


92 


48 


68124 


68214 


68304 


68394 


68484 


68574 


68663 


68752 


68842 


68930 


90 


49 


69020 


69108 


69196 


69284 


69372 


69460 


69548 


69635 


69722 


69810 


88 


50 


69897 


69983 


70070 


70156 


70243 


70329 


70415 


70500 


70586 


70671 


86 


51 


70757 


70842 


70927 


71011 


71096 


71180 


71265 


71349 


71433 


71516 


84 


52 


71600 


71683 


71767 


71850 


71933 


72015- 


72098 


72181 


72263 


72345 


82 


53 


72428 


72.509 


72591 


72672 


72754 


72835 


72916 


72997 


73078 


73158 


81 


54 


73239 


73319 


73399 


73480 


73559 


736.39 


73719 


73798 


73878 


73957 


80 


55 


74036 


74115 


74193 


74272 


74351 


74429 


74507 


74585 


74663 


74741 


78 


56 


74818 


74896 


74973 


75050 


75127 


75204 


75281 


75358 


75434 


75511 


77 


57 


75587 


75663 


75739 


75815 


75891 


75966 


76042 


76117 


76192 


76267 


75 


58 


76342 


76417 


76492 


76566 


76641 


76715 


76789 


76863 


76937 


77011 


74 


.59 


77085 


77158 


77232 


77305 


77378 


77451 


77524 


77597 


77670 


77742 


73 


60 


77815 


77887 


77959 


78031 


78103 


78175 


78247 


78318 


78390 


78461 


72 


61 


78533 


78604 


78675 


78746 


78816 


78887 


78958 


79028 


79098 


79169 


71 


62 


79239 


79309 


79379 


79448 


79518 


79588 


79657 


79726 


79796 


79865 


70 


63 


79934 


80002 


80071 


80140 


80208 


80277 


80345 


80413 


80482 


80550 


69 


64 


80618 


80685 


80753 


80821 


80888 


80956 


81023 


81090 


81157 


81224 


68 


65 


81291 


81358 


81424 


81491 


81557 


81624 


81690 


81756 


81822 


81888 


67 



* Each log is supposed to have the decimal sign before it. An error of 
less than 1 in the final decimal exists in a number of the logs of this table, 
it will not, however, be material in ordinary computations. 



200 



TABLE NO. 78. 



IiOg'aritbins of Numbers, 


from to 1000*— (Continued.) 


No. 


O 


1 


2 


» 


4 


j 
5 


« 


7 


8 


9 


Prop. 


66 


81954 


82020 


82085 


82151 


82216 


82282 


82347 


82412 


82477 


82542 


66 


67 


82607 


82672 


82T36 


82801 


82866 


82930 


82994 


83058 


83123 


83187 


65 


68 


83250 


83314 


83378 


83442 


83505 


83569 


83632 


83695 


83758 


83821 


64 


69 


83884 


83947 


84010 


84073 


84136 


84198 


84260 


84323 


84385 


84447 


63 


70 


84509 


84571 


84633 


84695 


84757 


84818 


84880 


84941 


86003 


850e4 


62 


71 


85125 


85187 


85248 


85309185369 


85430 


85491 


85551 


85612 


85672 


61 


72 


85733 


85793 


85853 


85913185973 


86033 


86093 


86153 


86213 


86272 


60 


73 


86332 


86391 


86451 


86510 


86569 


86628 


86687 


86746 


86805 


86864 


59 


74 


86923 


86981 


87040 


87098 


87157 


87215 


87273 


87332 


87390 


87448 


58 


75 


87506 


87564 


87621 


87679 


87737 


87794 


87852 


87909 


87966 


8!-024 


57 


76 


88081 


88138 


88195 


^8252 


88309 


88366 


88422 


88479 


88536 


88592 


56 


77 


88649 


88705 


88761 


88818 


88874 


88930 


88986 


89042 


89098 


89153 


56 


78 


89209 


89265 


89320 


89376 


89431 


89487 


89542 


89597 


89652 


89707 


55 


79 


89762 


89817 


89872 


89927 


89982 


90036 


90091 


90145 


90200 


90254 


54 


80 


90309 


90363 


90417 


90471 


90525 


90579 


90633 


90687 


90741 


90794 


54 


81 


90848 


90902 


90955 


91009 


91062 


91115 


91169 


91222 


91275 


91328 


53 


82 


91381 


91434 


91487 


91540 


91592 


91645 


91698 


91750 


91803 


91855 


53 


83 


91907 


91960 


92012 


92064 


92116 


92168 


92220 


92272 


92324 


92376 


52 


84 


92427 


92479 


92531 


92582 


92634 


92685 


92737 


92788 


92839 


92890 


51 


85 


92941 


92993 


93044 


93095 


93146 


93196 


93247 


93298 


93348 


93399 


51 


86 


93449 


93500 


93550 


93601 


93651 


93701 


93751 


93802 


93852 


93902 


50 


87 


93951 


94001 


94051 


94101 


94151 


94200 


94250 


94300 


9-1349 


94398 


49 


88 


94448 


94497 


94546 


94596 


94645 


94694 


94743 


94792 


94841 


94890 


49 


89 


94939 


94987 


95036 


95085 


95133 


95182 


95230 


95279 


95327 


95376 


48 


90 


95424 


95472 


95520 


95568 


95616 


95664 


95712 


95760 


95808 


95856 


48 


91 


95904 


95951 


95999 


96047 


96094 


96142 


96189 


96236 


96284 


96331 


48 


92 


96378 


98426 


96473 


96520 


96567 


96614 


96661 


96708 


96754 


96801 


47 


93 


96848 


96895 


96941 


96988 


97034 


97081 


97127 


97174 


97220 


97266 


47 


94 


97312 


97359 


97405 


97451 


97497 


97543 


97589 


97635 


97680 


97726 


46 


95 


97772 


97818 


97863 


97909 


97954 


98000 


98045 


98091 


98136 


98181 


46 


96 


98227 


98272 


98317 


98362 


98407 


98452 


98497 


98542 


98587 


98632 


45 


97 


98677 


98721 


98766 


98811 


98855 


98900 


98945 


98989 


99033 


99078 


45 


98 


99122 


99166 


99211 


99255 


99299 


99343 


99387 


99431 


99475 


99519 


44 


99 


99563 


99607 


99651 


99694 


99738 


99782 


99825 


99869 


99913 


99956 


44 



* See foot note on pa^e 199. 



The log of 2870 is 3.45788 
" " " 287 is 2.45788 
" " " 28.7 is 1.45788 
" " " 2.87 is 0.45788 



The log of .287 is — 1,45788 

" " " .028 is — 2.44716 

" " " .002 is — 3.30103 

" " " .0002 is — 4,30103 



Whatis thelogof 2873? 

Here, log of 2870 = 3.45788 
And prop 153 X 3 = 459 



3.458339 



To find roots divide the log (with its index) of the given number, by that 
Bomber which expresses the kind of root. The quotient will be the log of the required root. 
£x.ailiple. What is the cube root of 2870 ? 

Here, the log of 2870, with its index, is 3.45788. And = 1,15263. Hence the cube root is 14,2, 

The Hyperbolic, or Xapierian log-aritbin is the common log of 

the table multiplied by 2.3025851. 

Sq. rt, 6925=Log 3. 84042 -4-2= log 1.92021, corresponding No.=83.2138=sq. rt" 
Cu-rt.6925= " 3.84042-4-3= " 1.28014, " " =19.0669=cu. rt. 

4th rt. 6925=" 3.84042-5-4=" -96010, " " = 9.1222=4th rt. 

Proceed in like manner for any other root required. This method of ex- 
tracting roots is more rapid and simple than any other. 



201 



EXPLANATION AS TO TABLES OF LOGARITHMS. 

LO G A R I T H M S are the exponents with which a fixed number must be 
affected in order to produce a given number. The fixed number is called 
the BASE. The base of the common system of logarithms is 10. 
Since 10" = 1 the logarithm of 1 is 0. 
" 10^ = 10 " " " 10 " 1. 

" 102 ^ 100 " " '• 100 " 2. 

Thus, the logarithms of all powers of the base are integral numbers., 
while the logarithms of numbers intervening between exact powers of the 
base are composed of an intiger and a fractional or decimal part— called 
the MANTISSA. The integral part of the logarithm being called the 

INOFX orlcHARACTERISTIC 

NOTE WELL THE FOLLOWING RULES. 

I. The log. of any exact power of 10 is a positive (+) intiger 
one less than the number of places in the namber. 

Thus— See figures at foot of table on page 200— 
Log of 2870 has 3 for its index, there being 4 figures in the number. 

■ ■ — ■ ~ ' " " " 3 " " 

( (. (1 (1 .^ li (i .( 

i u (C (( 1 ti (. C( 



287 ' 


• 2 


28 ' 


• 1 


2 ' 


' 



II. The characteristic of any decimal number is negative 
(— ) and numerically one t)iore than the number of zeros 
immediately following the decimal point. 

Thus — See figures on page 200 (2d column.) 
Logoftdecimal .287 (being no zeros) = — 1. C Negative, and 1 in excess of 
" " " .028 ( " 1 zero ) = — 2. < the number of zeros immedi- 
" " '• .002 ( " 2 zeros] = —3. (ately following deci'al point. 
( The minus sign][instead of being placed befori the index, as ? 
^ here shown, is usually placed above thei ndex, thus, 3. ' 



USE OF TABLE. The logarithms of numbers from 1 to 9 are taken 
from the top horizontal line of the table, Log of 9 being .95424 ; and logs of 
numbers from 11 to 99 are taken from the first column, headed by O, the 
index 1 being added as above explained [IJ. Thus— the log of 91 = 1.95904, 
Log of 80 = 1.90309. Logs of numbers from 100 to 1000 are taken from the 
table as follows— required the log of 915 ; find 9i in first column and then 
run horizontally across the table to the column headed 5 where is found 
the log .96142 to which add an index of 2, as above explained, making 
2.96142 the log required. Log of 800 would in like manner be 2.90309, log 
of 801 = 2.90363. Since the decimal part of the logarithm is not changed by 
multiplying or dividing the number by any power of 1<9 the logarithm of a 
number of 4 or 5 places may also be taken from the table as shown at the 
foot of the table. The log of 287 = 2.45788 and log of 2870 = 3.45788— the 
index only being changed. If, however, the 4th figure is other than O, as 
2873, then proceed as follows :— find the log of the 3 left hand figures and in 
the same horizontal line, at its intersection with the last vertical column, 
headed ''Prop." [Proportionate parts] take the number indicated and 
multiply it by the last figure of the given number . Exclude one figure 
from the product and add the remainder to the log first found. In case 
as shown at foot of table log is taken for 2870 then in last column is found 
153 which X 3, the last number of the given number 2873, exclude the right 
hand figure from the product of 4.59 and add the remainder, 45, to the log 
first found. 



What is the log of 28735? 
Here log of 28700 = 4.45788 
And prop 153 X. 35 = 53.55 

Log of 28735 =4.45841 



Here 2 figures are cast off because there 
are 2 figures in the multiplier [35] . With 
numbers of 5 figures this may be in error 
1 in the last decimal. 



202 

In the use of logarithms it is not only necessary to find the log corres- 
ponding to a given number but also to find the number corresponding to 
any given log. 

III. Given any log to find the corresponding number. 

Pi.— Where the- mantissa is found in the table. 

Look in the table for the given log, take out the corresponding number 
and place the decimal point according to the given index. 

Example — Given log 4.96142, what is the corresponding number? 

Look in table for log 96142 and find it corresponds to the number 915. 
The given index 4 indicates a number of 5 places therefore point off the 
number obtained to have 5 places and to read 91500. 

Log of 2.90309 corresponds to 800 ; Log .30103 to 2. &c. 

B.— Where the mantissa is not found in the table. 

Take from the table the next lesser mantissa and its corresponding num- 
ber. Then subtract this mantissa from the given one and divide the re- 
mainder by the number opposite in the column " Prop." Annex the quo- 
tient so found to the tabular number taken out and then point off as indi- 
cated by the given index. 

Example — Given the log 1.96166 to find the corresponding number. 

From table we find .96142 to be the nearest lesser mantissa and 915 to be 
the corresponding number. .96166, the given mantissa, minus .96142 the 
lesser one = difference of 24 which being divided by 48, the number found 
in column " Prop." — .5. This being annexed to the tabular number 915= 
9155. The given index 1 indicates a number of 2 places, so 91.55 becomes 
the required number. 

THE USE OF LOGARITHMS. 

The ADDITION of logarithms corresponds to ordinary[,'MULTI PLICA- 
TION and any number of given numbers either integral, decimal or mixed, 
may be multiplied together by one operation. 

Thus : multiply together 166, 71.5, 8.25 and .078 (=7637.7). 
Log 166. = 2.22010 

Note. The index of the last log being 
minus it is subtracted from the sum of the 
+ indices, 5, leaving 3 the index of the sum. ) 



71.5 = 1.85430 
.25 = 0.91645 

.078 = —2.89209 



" of product =3. 88294 

By method B, above given, the log 3.88294 is found to correspond toTthe 
number 7637. 7 which is the required product. 

The SUBTRACTION of logarithms corresponds to ordinary'DIVISION. 
The log of the divisor being subtracted from the log of the dividend gives, 
as a remainder, the log of the quotient. 

Thus— Divide 86.32 by 6.85 (=12.601) . 
Log 86.32 = 1.93611 

" 6.85 = 0.83569 



" quotient= 1.10042, which, by method " B," = 12.601 ="quotient. 

TO RAISE A NUMBER TO A POWER. 

Rule.— Multiply the log of the number by the exponent of the power and 
find the number corresponding to the product. 

Thus— What is the 5th power of 7.65? 

Log of 7.65= .88366 which X 5 = 4.41830 the number corresponding" to 
which is 26200. 

TO FIND ANY ROOT BY LOGARITHMS. 

See explanation at foot of table on page 200. The cube root 14.2 being 
the number corresponding to log 1.15263. Proceed in like manner for any 
other root required. 



203 

The foregoing explanations as to the use of logarithms are cheifly for 
the benefit of those who have, by disuse, become ''rusty" in the use of the 
tables ; although any one may in a day or two become f amilliar with 
them and may, by their use, greatly lessen the drudgery of mathematical 
calculations. Such uses only have been explained as pertain to the sim- 
pler mathematical operations. 



EXPLANATION OF CHARACTERS, 



The following brief explanation is given of a few of the more com- 
mon characters used in calculations, etc. and which are so frequently 
met with in mathematical and similar works. 



= Signifies 

+ 
X 



Equality, 

Plus, 

Multiplied by, 

Minus^ 

Divided by, 

Proportion, 
so is 4 to 16, 



( ) [ ] 



z 
1 

A 

D 

o 



Tt 



> < 

00 



h I &c. " 
i I f «&c. " 



&c. 



as 2 + 2 = 4. 
as 2 + 2 = 4. 
as 2 X 4 = 8. 
as 8 — 2 = 6. 

as 8 -i- 2 = 4. 

as 2 : 8 : : 4 : 16 reads . 
or, 2 is to 8 as 4 is to 16. 



, as 2 is to 8 



Signifies 



The Viiiculum or Bar indicates that all the numbers 
over which it is pla ced are to be consid ered as one 
quantity, thus, 2 + 8 -^ 2 = 5 ; or 5 X 8—2 = 30. 
Parenthesis or^ Brackets indicate, as in above, that 
all included figures are to be considered as one quan- 
tity, thus, ( 3 X 5 ) + 10 = 25 ; or 3 X [ 5 + 10 ] = 45. 
Decimal Point. 

The Radical or Root sign when placed before a num 

ber indicates that t he squa re root of the number is 

required, \ 16 = 4; \15 + 10 = 5. The degree of the 

root, other than the square root, is indicated by a 

figure placed above the radical, which figure is 

called the Index. V = Cube root ; V = 4^/1. root etc. 

Angle. 

Perpendicular. 

Triangle, or triangular as A iron or inches. 

Square, as □ " " " 

Circle or Circular, as O " " " 

Therefore or Hence. 

Because. 

The Ratio of the circumference of a circle to its diam- 
eter, which = 3.1416 . 

Greater and Less, a> b reads - a greater than 6. 
Infinity. 

Degrees. Minutes, and Seconds of arc. 

Feet and Inches. 

when set superior to a number, that the square or cube 

root etc. is wanted, thus 25^ indicates the sq. rt.of 25. 

when set superior to a number, respectively, the sq. rt. 

of the cube; the sq.rt. of the 5th. power; and the cube 

root of the 6th. itower etc. 

when set superior to a number, the power to which the 
number is to be raised, thus 2^5 = 4,' 2' = 8 ; 2^ = 32 &c. 



204 



CONCLUSION. 

The public may claim that the author owes to them an apology for hav- 
ing presented an irrigation manual wherein no direction is given as to the 
detail workings of an irrigation plant, or any direction as to when, and 
how often, to irrigate, how to prepare the soil, &c. Such was not the ob- 
ject, as stated in the preface, but rather to present certain items of techni- 
cal information, and such other matter as would tend to show the import- 
ance and practicability of irrigation in the Dakotas. The subject is one 
too vast to be treated fully in one volume, or in a score of volumes, such as 
this. More has been omitted than has been included, and much which 
was of value, and which it was desired to include, has been omitted be- 
cause of the limited means and space, and the circumstances under which 
this little book was made. Should it become advisable to issue a second 
edition many additional features of interest and of value will be included. 
A start has, however, been made which it is to be hoped others will more 
successftilly emulate until all of the people of these states shall have be- 
come imbued with the vital importance to themselves and to their child- 
ren of this matter of irrigation ; and until the thousands of acres of our 
now waste paradise shall have put on that cloak of perrennial verdure 
which is their due and their destiny. 

No more fitting conclusion can be made than to quote frora the eloquent 
words of the late Hon. S. S. Cox, congressman from New York, delivered 
in his oration at Huron on July 4th, 1889. Words as poetic in sentiment 
as they are prophetic of truth. He said : 

'• But yesterday your fruitful valley was whitened 
with the bones of the buffalo. Now it is an ideal 
farming area. It is a lesser Nile region, without its 
overflow. Artesian Wells give water where the sun 
once made drouth perrennial. The water power of 
your matchless valley is as yet immeasurable by 
ordinary mechanical standards. It is so prevalent 
that your people will utilize its specific gravity for 
the diversity of their industries. When its undi- 
minished flow and steady pressure from the bosom 
of the earth are properly harnessed by mechanism, 
it will give its lucid Ijonph to make grasses for 
stock and lawns for beautiful homes. Its sunless 
currents, through the ingenuity of man, will en- 
hance the rich soil by quenching its thirst. Fab- 
ulous are the wasted energies of your water power, 
as we count it by the standard horse power of me- 
chanics; but still more marvellous are the real 
energies of the soil which it woidd fructify. 

The beautiful and fruitful valley of the James 
may not be as redolent of historic association and 
traditions as another James River of the colonial 
days ; but deeper than historical or traditional in- 
cident are Dakota's pure springs under a magic 
more enchanting than that of Aladdin, which leap 
from j'our modern Artesium. 



The End. 



p[dY)ertising 5^p>pendix. 



The author, on behalf of the public for whom this Manual is in- 
tended and to whom it will come, acknowledges the obligation due to 
the advertisers herein; for from the proceeds of this feature of the 
book has, in chief, been derived the funds for its publication. Had 
it not been for this patronage the book could not have been made. It 
is hoped and expected that in no sense has this been a charity, but 
rather a good paying investment, for the goods advertised will be 
used in large quantities in these states and the advertisers deserve 
the patronage of our people not only because the largest and most 
responsible representatives in their respective lines, but because of 
the acknowledged excellence and reputation of the goods they rep- 
resent. 

The information contained in this appendix will be of value to ir- 
rigators and others who often find difficulty in learning ss to where 
to find reputable dealers with whom to deal. Such only have been 
solicited, and to such as are here represented our people fairly owe 
their patronage. 



206 



i 



B. Glow ^ 



LAKE AND FRANKLIN STREETS, 

CmC-A-O-O, - - II-i3LiI2?TOIS. 
Manufactxirers of and Dealers in 












3 IVrougkt Iron Pipe, 
\ Artesian Well Tubing, 

Well Casing^ 

Line Pipe, 

Boiler Tubes, 

Well Tools, 

Fittings & Brass Goods 






ALSO 



^applies for flambers, 
©as aind Steam ITitters and 
Water Wori^s. 



SEND FOR CATALOGUE AND PRICES. 



207 



WELL DRILLING MBGHINERY, 



MANUFACTURED BY 



Willian?3 BFother^, 

ITHACA, N. Y. 




A.WUGEORD.HFD.rT. 



Mounted and on Sills 



FOR 



Deep or shallow wells, 

WITH 

Steam or horse power.. 



SEND FOR CATALOGUE. 



Address 



^illiams I^potbers, 

ITHACA, N. Y. 



208 



Engineering News 



AND 



AMERICAN RAILWAY JOURNAL. 



Is published Every Thursday at the Tribune Building, New York 
City. It is a 60 page paper, was established in 1874, and it is the 
Pioneer in publishing the news of Engineering Construction 
Work throughout the Continent. It was the first journal in Ameri- 
ca to make a specialty of WATER WORKS construction and it 
still maintains its lead in that large and growing interest over all its 
competitors. 

Engineering News was the first American journal which paid 
particular attention to the subject of II^^IGATION, and it has 
published more valuable information on this important interest of the 
arid regions of the west than all other American papers combined. 
It was the only Engineering journal in America specially represented 
at the Irrigation Congress recently held in Salt Lake City, and 
it is now the only paper East of Denver which is interested in the 
great question of Irrigation. 

Engineering News is a national journal; it circulates in every 
state and territory on the American Continents — from Alaska to the 
Argentine Republic; it is read by more contractors and hydraulic 
engineers than all other engineering newspapers combined and is an 
especially favorable medium for advertising PROPOSALS FOR 
IRRIGATION WORKS to be constructed in the West. 

The price of the paper is $5.00 per year; the cost of advertising 
proposals for contracts is 20 cents per line of seven words to the line. 

If you want to get the services of the best contractors for the low- 
est price try an advertisement in Engineering News. 



address 



ENGINEERING NEWS PUBLISHING CO., 

TRIBUNE BUILDING, NEW YORK. 



209 



H Great Work oi? iFFigation. 

A magnificent double volume containing 
over 800 pages devoted to irrigation progress in 
every land. The most complete work ever 
published; containing over 200 valuahle cuts. 
This great book, entitled ^'Irrigation Canals and 
other Irrigation Works'' and "Flow of Water 
in Irrigation Canals " is now ready for distribu- 
tion. It is written by P. J. Flynn, the famous 
engineer of California. Engineers, Investors 
and all who are interested in irrigation should 
have this book. Price for both volumes $8.00. 
Send your order to 

Tfbe [ppigation J^LS^, 

gait nal^e Qity, U«ab. 



THE IRRIGATION AGE. 

ffihE PionEEF iFFigation Journal ol tl^E World. 

PUBLISHED SEMI-MONTHLY BY THE 

Bmytl/E, Bpitton Ji^ Poofe Go, 

Offices: 
Salt Lake City. San Francisco. 

Denver. Washington. 



Invaluable to extevy farmer of Qal^ota. 



SuBSCBiPTiON Price, $2.00 per year. 



210 



GHBPMBN VALUE MBNFG, GO. 



Works and General Office, 
Indian Orchard, Mass. 
JASON GILES, Gen, Mgr. 



Treasurer's Office, 
72 Kilby St., Boston, Mass. 
C. J. GOODWIN, Treasurer. 



Chicago Office, 24 W. Lake St. E. W. BUSS, Western Mgr. 




GATE VALVES 

for steam or water. Also 

Fire {jydrant?. 

THE CHAPMAN VALVES ARE THE BEST 
AND MOST DURABLE MADE. 



A full stock always on hand in Chicago 
Give us a trial. 



211 

THE CHICAGO 

* WATER MOTOR * 

For running by Artesian Wells or Hydrant Pressure, Sewing Ma- 
chines, Dental Lathes, and Engines, Organs, Printing Presses, Saus- 
age Machines, Coffee Mills, Corn and Feed Mills, Ventilating Fans, 
Ice Cream Freezers, Elevators, Electric Lights, &c. 

We have more motors in use IN DAKOTA, than all other makes 
combined. 

''Huronite,^' Huron, S. D., May 8, 1890. 
Gents: 

Your Double Motor we regard as an improvement over the Tuerk. 

Signed: Shannon & Longstaff. 

(The above after using a Tuerk Motor 2 years purchased one of 
ours.) 

Watertown, S. D., May ist, 1890. 
Gents: 

We are using one of your No. 1 1 Double Motors for driving Pony, 
cylinder and job press — pressure 60 lbs. Our former superintendent 
put a Little Giant motor in our office but we found that this motor, 
when running only one press, used more water than yours when run- 
ning two presses; and, even with the larger consumption of water 
was not able to run both presses. 

Signed: CoNKiJN & Reddick, 

Publishers, Conklin's Dakotian. 

WE WILL MAKE 

-^^LOWER PRICES--^- 

THAN ANY OTHER 

first Glciss TVlotop. 

CAN ALSO SELL YOU A 

WIND MILL 

and the best GRINDING MILL in the market. 

Address 

Ghicago Water RBotoF Gompany, 

101 LAKE ST., CHICAGO. 



212 



ST. LOUIS 

WELL "^lir^ CO., 

ST. LOTJIS, IMIO. 



MANUFACTURERS OF 



WELL MACHINERY, 

WELL TOOLS, 

WELL SUPPLIES. 



C^T.A.I_,Oa-TJE IF'K.EE. 



Address, 

St. Louis Well Machine & Tool Co. 

Wabash Track and Newstead Ave. (South 44th St.,j 
ST. LOUIS, MO. 



213 



We find it to oilr interest to bilu 

WROUGHT IRON PIPE 

for steam gas and water, also 

CRSlliG, 

IaIhyi pips, 

DRlY^i PIPS, 
Boiler T-tfoes, 
h.G., kc' 

FROM 



^Bli 


1 6. W. CRANE 


j 




B WholEgalE BealErg. 


h 




H MINNEAPOLIS. MINN. 


II 




^M SVe also carry ^ 


J^B 


f 


■ Tbe Most Complete Stock gj 


b.SAUJDERS'SOhS-n 
kPAT.Na».23 laao. ^ 




1 STYIRM'GOODS^ 


^©JB 




H in the Northwest. ^I^B 





Send for Illustrated Catalogue. 



214 



Rife's Hydraulic Engine 
(or Ram.) 

Patented February 8, 1887. 

For supplying water to Small Towns, Factories, Steam Mills, Daries, 
Stock Yards, Railway Tanks, Residences, and for 



View of ram. 
Send for Catalogue. 




Constructed on new and improved principles, greatly increasing 
the capacity and avoiding extreme concussion that has heretofore 
proved destructive to all common Hydraulic Rams, making this 

Especially Adapted 
to Railroad Water Supply and Irrigation . 

The following is an extract from a letter to the company from a 
gentleman who is using one of these rams to water over 12 acres of 
trees: 

Orovili-e, California, Dec. 10, 1890. 

The machine is doing better work now than ever before, discharg- 
ing about 25 gallons per minute or the enormous amount of 36,000 
gallons per day. Signed: D. B. Hays. 

Write for illustrated catalogue, to 

Rife's ]§\;draulic Gngine TYl^S* G^m 
ROANOKE, VIRGINIA. 

(See page 124 of this book.) 



215 

BUFF x& BERBER, 

IMPROVED 

BQ^ineerglng ana UmH Instilments, 

Nio. 9 Province Coiart, Boston, Mass. 

They aim to secure in their Instuments, — Accuracy of division; 
Simplicity in manipulation; Lightness cojubined with strength; AchrO' 
matic telescope, with high power; Steadiness of adpistments under vary- 
ing temperatures ; Stiffness to avoid any tremor, even in a strong wind^ 
and thorough workmanship in every part. 

Their instruments are in general use by the U. S. Government 
Engineers, Geologists and surveyors, and the range of instruments, 
as made by them for River, Harbor, City, Bridge, Tunnel, Railroad 
and Mining Engineering, as well as those made for Triangulation or 
Topographical Work and Land Surveying^ is larger than that of any 
other firm in the country. 

Illustrated Manual and Catalogue sent on application. 



TRAUTWINE'S 

Civil Engineer's Pocket Book. 

"If you can own but a single book let it be this, and by all means 
have this if you are but a rodman, if you intend to continue in the 
work." — Railway Age, Oct. 9, 1884. 

"Without doubt it has proved itself to be the most useful hand- 
book in the language for the Engineering profession." — Engineering 
and Mining Journal, .Aug 25, 1888. 

"The best general text-book on civil engineering in the English 
language. It is a whole library in itself." — Engineering N'ews, Jan. 
27th, 1883. 

"It is a book for the civil, mechanical, hydraulic and mining en- 
gineer, and architect and builder. Its tables are invaluable, and al- 
most absolute reliance can be placed in them." — Engineering atid 
Building Record, Aug. nth, 1 888. 

"It is, deservedly, one of the most popular of Pocket Books, be- 
cause the information it contains is presented in such plain terms as 
to be readily comprehended by those who have not had the advant- 
ages of a technical education. Every statement is in the fewest 
words that will clearly convey the meaning." — American Machinist, 
May 9th, 1885. 

For sale by John Wiley & Sons, 53 East 10th St., New York City, 
or by J. C. Trautwine, Jr., 3301 Haverford St., Philadelphia, Pa. 

PRICE, $500. 



216 



nidpton Pipe & Steel Co., 

CINCINNATI, 0. 

ItJP 



FOR 



Qalverts, 
§ewers 

ANi-IrrigeLtion. 



WATER PIPE, 
GAS PIPE. 



Ga^tiijgg ol Syefij BegcFiption, 

WRITE US FOR ESTIMATES. 



2r 




218 



F, G. I1U8TIN HIFG. GO., 



MANUFACTURERS OF 



ARTESIAN 

WELL DRILLING 

MA CHINER Y. 

Pole Tool Rigs. 
Cable Rigs. 
Hydraulic Rigs. 
Jetting Rigs. 
Turning Rigs 

AND 

Combined Rigs- 

ALSO 

Drilling Tools 
I and Supplies. I 




F, G, AUSTIN MHNFG, GO, 



CARPENTER ST. & CARROLL AVE. 

CHICAGO, - - - - ILLINOIS. 

(Seepages 117 , 118 & next page.) 




New Era Grader and Ditcher 

New Era Grader, Ditcher and Wagon Loader, for building 
irrigation canals and storage reservoirs is guaranteed capable of plac- 
ing in the embankment looo to 1500 cubic yards of earth in 10 hours 
with 6 teams and 3 men, at a cost not exceeding 2 cents per yard; and 
©f wagons 600 to 800 loads of i^- yards per load in the same time. 
The Best Machine for building 

^^^IRRIEATIQN DITCHES. 




Austin Steel Reversible Road Machine. 

Austin's Steel Reversible Road Machine, for making lateral ditches 
and building country roads, will build I4 mile of lateral ditch per day. We 
also make Dump Wagons : Wheel, Drag and Buck Scrapers and Contract- 
or's Plows. Send for catalogue to the 

F. C. Austin Manfg. Co., Chicago, 111. ^^'Tc^'rrou Ave'' ^'- 



220 

W. & L. E.GURLEY, 

TR.03r, 3sr. Y. 

Largest manufacturers in America of Civil Engineers' and Sur- 
veyors' Instruments; our latest illustrated price list on application. 

THE ARCHITECT'S LEVEL. 




Price as shown, with tripod, $50.00. 

This figure represents the level introduced by us in 1874, and 
which has since been very largely used by architects, builders, en- 
gineers, and surveyors, in the grading of streets, drives, sewers, etc., 
in all parts of the country. 

It has a telescope 12 inches long, furnished with rings, wyes, etc, 
precisely like our larger levels, and adjusts in the same way. 

The leveling head has the ordinary screws and a clamp to the 
spindle; it has also a horizontal circle 3 inches in diameter, fitted to 
the upper end of the socket, and turning readily upon it; the circle 
is graduated te degrees, figured from o to 90 each way, and is easily 
read to five minutes of a degree by a vernier which is fixed to the 
spindle. 

The adjustments are not liable to derangement, and ordinarily re- 
quire but little attention. 



1^E."\I^1^S \ 



221 



TROY, N. Y. 

FARMER'S OR DRAINAGE LEVEL. 




Price, as shown, with tnpod, $25.00. 
This Level combines the extremes of simplicity and compactness 
with real efficiency, and at moderate cost. The telescope, 9 inches 
long, is achromatic, and of sufficient power. The cross wires are 
not easily disturbed. The level and telescope are both inclosed in 
an outer bronze case. The instrument is approximately leveled by 
the ball spindle on the socket and then precisely so by ihe levelmg 
screws. The advantage of this form of Level in the work of the 
farmer in laying out ditches and reservoirs will be apparent on in- 
spection. When desired we add to this level a .3-inch needle mag- 
netic compass at an extra cost of $5. This is fitted to the case as 
shown below and can be removed at pleasure. 




222 




223 



WELL MACHINERY. 



Send for our Catalogue 

DESCRIBING A FULL LINE OF 

ARTESIAN WELL OUTFITS, 
PORTABLE ROCK DRILLS, 

AND THE CELEBRATED 

PEch Well RuqEY, 

WIND MILLS, 

GENERAL WELL SUPPLIES, 
&c.. &c. 



THE PECH MFG. CD., 

SIOUX CITY, IOWA. 



224 



Valve Manufacturing Co., 



MANUFACTURERS OF 



Valves ai/d Fire F^ydpar/b 




Double and Single Gate 

VALVES, 

ALSO 

Check Valves, 
Foot Valves, 

and Yard and Wash 

HYDRANTS- 





FACTORY AND OFFICE. 

9 3 8 to 9 54 River St ., and 6 7 to 8 3 VaiJ Ave ., 

TROY, N.Y., U.S.A. 

^"SEnSTID FOE. OIK.OXJIj.A.I^S- 



225 




WELL DRILLING 

MACHINERY, 

AND TOOLS, ADAPTED TO ALL KINDS 

of work, and prospecting. 

Horse and Steam Power. 
They never faiL They are Sim- 
ple, Practical, and Thorough. 

We also make 
a full line of gas and 

Water Works Goods, 
Gate Valves, & Hydrants. 



Our open-way hydrants are the 
best in the market. 

Corporation Cocks, 

and the best 

Tapping Machine 

in the world . 




Write for Circalars, and let us talk 
it over with you. 

Address the 

Brassilron Works Co. 

FOSTOIIIA, OillO. 



226 



THE PELTON WATER WHEEL. 

Affords the most efficient and reliable power for all purposes, be- 
ing especially adapted to utilize the power from ARTESIAN 
WELLS. They are warranted to give from 25 to 40 per cent better 
results than any other wheel. The Woonsocket and Yankton Mills 
and Huron Electric Lights are run with Pelton wheels. 

(See page 81.) 

PELTON WATER MOTORS, 

embrace the smaller wheels set in iron casings ready for pipe connections 
Made of capacities from a fraction of 1, up to 50 horse power. The cheap 
est and, most convenient power. Parties interested in the development of 
Dakotas great artesian power will be furnished with catalouge, circulars, 
and other information on demand to the 







227 



Oil Well Supply Co., 

PITTSBURGH, PENN. 

Manufacture every article, tool or appliance 

needed at 

ARTESIAN WELLS. 



ARTESIAN 

WELL 
MACHINERY. 




Boilers, ^i\gmes,PMraps, 
DerriG"ks, Cordage, ?\\;Ungs, 
DriWmg and "FisYimg Tools, 
TAibmg and Casltig. 

BFa^3 and iFon Good^ and Bupplieg. 

For Steam, Gas, Petroleum or Water. Catalogues and Price Lists 

on application. 



228 

W. E. SWAN. p. J. STAGEY. 

W. E. SWAN CO., 

ANDOVER, S. D. 

Drilled the first well in Dakota, at Aberdeen. 



Have had TEN YEARS' experience IN DAKOTA. 

Being the oldest drillers in the state, and 
having the most experience in the hard Dako- 
ta formations, and the best rigs and most im- 
portant tools we are better equipped for rapid 
and successful work than any drillers in the 
Dakota basin. Our experience extends over 6 
states and our record is as good as our experi- 
ence is broad and varied. We are prepared to 
drill to any depth and of any size. Among our 
wells are the following: 

WELLS IN N. AND S. DAKOTA. 

Aberdeen, _ __ 

Columbia, . . 
Groton, ■ 6 'wells in Manitoba. 

Andover, Manxin Minnesota. 

Ashton, " " Wisconsin. 

Huron, " " Iowa. 

Mellette, '' '' Illinois. 

Devils Lake, 

Bismarck, 



Grafton, 
Frankfort, 
Ipswich, 
Aud many farm wells 
in both states. 



Correspondence solicit- 
ed, (live us a chance 
to bid on your work if 
you want good work 
and promptly done. 




cc uj fie 

UJ I -i UJ 

oc o 5 t < 



230 



The Great Northwest 

is traversed by the 

Chicago & Northwestern 
Railway. 

The finest cars in the land are run on its 
trains between Chicago and all the principal 
points in 

ILLINOIS, 



WISCONSIN, 
MINNESOTA, 




NEBRASKA, 
SOUTH DAK., 
AND IOWA. 



Chicago, 
St. Paul, 
Ashland, 
Council Bluffs, 
Sioux City, 
Huron, 
Aberdeen, 



Milwaukee, 
Minneapolis, 
Superior, 
Omaha, 
Sioux Falls, 
Watertown, 
and 
are all reached by our lines. 

Parties desi];ing to visit the great 

ARTESIAN BASIN 

of Dakota should take this line for all the great artesian 
wells are reached by our road. 



Madison, 

Duluth, 

Winona, 

Des Moines, 

Mitchell, 

Pierre, 

Oakes. 



The best farming land in America is to be had in 
the Dakotas where IRRIGATION BY ARTE- 
SIAN WELLS will make every farmer rich. 



231 



Profitable Investments. 



the chicago and 

North ■ Western 
railway co. 

Owns Lots in most of the Cities and Towns on itsjlines in 

SOUTH DAKOTA. 



These Lots are For Sale 

at such prices and terms as to secure to purchasersj^safe and 
profitable investments. 



South Dakota is All Right, 

and those seeking locations for investments, or opportunities 

for the investment of capital, should give it an 

intelligent investigation. 



For particulars apply to 

CHAS. E. SIMMONS, 

Land Commissioner C* & N.-W. Ry. Company, 
CHICAGO, ILLINOIS. 



232 



A GREAT RAILWAY. 

The Chicago, Milwaukee & St, Paul Rail- 
way Company now operates over sixty-one hun- 
dred miles of thoroughly equipped road in Illinois, 
Wisconsin, Northern Michigan, Minnesota, 
Iowa, Missouri, South and North Dakota. 
Each recurring year its lines are extended in all di- 
rections to meet the necessities of the rapidly popu- 
lating sections of country west, northwest and 
southwest of Chicago, and to furnish a market for 
the products of the greatest agricultural and stock 
raising districts of the world. In Illinois it operates 
317 miles of track; in Wisconsin 1,636 miles; in 
Northern Michigan 96 miles; in Iowa 1,551 miles: 
in Minnesota 1,115 n^iles; in South Dakota 1,092; 
in North Dakota 118 miles; in Missouri 140 miles, 
and the end is not yet. It has terminals in such 
large cities as Chicago, Milwaukee, La Crosse, 
St. Paul, Minneapolis, Fargo, Soiux City, 
Council Bluffs, Omaha and Kansas City and 
St. Joseph, Missouri, and along its lines, are hun- 
dreds of large and small thriving cities, towns and 
villages. Manufacturing interests are cultivated, 
and all branches of trade find encouragement. The 
Railway Company has a just appreciation of the 
value of its patrons, and its magnificent earnings 
are the result of the good business tact which char- 
acterizes the management of its affairs. 



233 

THE POPULARITY OF THE 

Gblcago, Milwaukee and St. Paul 

Railway 

is attested by the fact that notwithstand- 
ing the strongest kind of competition of 
old and new lines, the Chicago, Milwaukee 
& St Paul Railway continues to carry the 
greater proportion of all the business be- 
tween Chicago, Milwaukee, St. Paul and 
Minneapolis. It is the best patronized 
route between Chicago, Council Bluffs 
and Omaha and to and from all points in 
Wisconsin, Minnesota, Dakota and Iowa, 
and its Kansas City and St. Joseph Hne 
has taken equal rank with the older lines 
leading to and from the Southwest. 

On all its through lines of travel the 
Chicago, Milwaukee & St. Paul Rail- 
way runs the most perfectly equipped 
trains of Sleeping, Parlor and Dining 
Cars. The through crains on alJ its lines 
are systematically heated by steam. 
No effort is spared to furnish the best ac- 
commodations for the least money, and, in 
addition, patrons of the road are sure of 
courteous treatment from its employes. 



234 
THE 

Engineering Magazine 

A high-class, beautifully illustrated monthly magazine, 
like the ( Century and Harper's, but devoted exclusively to 
industrial affairs and engineering problems. It covers the 
entire field of industry, and besides nine special depart- 
ments, and a monthly index to all that is of value in tech- 
nical literature, each number contains ten leading articles 
by distinguished authorities upon topics that are uppermost 
in public interest. 

The following are among the leading articles published in 
recent numbers : 

Progress in Aerial Navigation, (Illustrated) 

O. Chanute, president American Society C. E. 

The Future of our Wagon Eoads— Wm. Claypoole, C. E. 

The Solution of the Block Signal Problem, (111.) 

H. Ward Leonard, E. E. 

Is the limit reached in armored Warships ? 

Albert Williams, Jr., E. M. 

Pure Water and Public Health. 
Eloyd Davis, Ph. D. Chemist, Iowa State Board of Health. 

The Canadian Pacific Eailroad— T. K. Thomson, C. E. 

Worthless Government Engineering--Geo. T. Wisner,C. E. 

Followed by a criticism by Lieut. Col. W. E. King of the 
Engineer Corps, and a rejoinder by the author. 

The World's Store of Tin, (111.) E. W. Claypole, A. B., D. Sc. 

The Eights of the Lowest Bidder; What the Contractor 
Wants to Know, L. Allen, A. B., M. E. 

The Answer of the Law, C. E. Hellier, LL. B. 

The Decline in Eailroad Building, T. L. Greene. 

The Wind as a factor in Geology (111.), G. P. Merrill. 

The Manufacture of Ice, L. Allen, A. B., M. E. 

The Purification of Water, P. Davis, Ph. D. 



"Edited with marked ability."— Posfon Herald. 

"Readable from cover to cover."— India?iapoZts News. 

"Studded with ideas of practical value."— iVbr/oZfc Virginian. 

"The contributors are men of the highest rank."— S^. Louis Republic. 

"We heartily commend it to the general public." — Boston Transcript. 

"Unquestionably the most elaborately illustrated engineering journal 
that has yet appeared on either side of the Atlan tic. "—Ifec^amcaZ World 
London. 

Price— 25 cents a number; S3.00 a year. At all news 
stands, or by mail. Send 10 cts. for a sample copy, and men- 
tion this manual. 

THE ENGINEEEING MAGAZINE CO., 

World Building, NEW YORK, U. S. A. 



235 



Great Northern Ry. 

Has 3 lines in South Dakota, connecting 

Sioux Falls, Huron, Watertowii and Aberdeen 




WITH 



St, Paul, 
Minneapolis, 
Dttlutli, 
Superior 

AND THE 

EAST. 

Reaches more 
points in 

Minnesota, 

AND 

Kortli Dakota 

than any other 
line. 



Has 2 Lineis 

from St. Paul and 

Minneapolis 

to the 

DESed lESi Trer T 7"a>lle37' - 

It is the direct route to GREAT FALLS, HELENA and 
BUTTE. Gives choice of TWO ROUTES TO THE PA- 
CIFIC COAST. Round Trip Tourist Tickets to all the 
leading points in the west. For Maps, publications and in- 
formation apply to any agent of the Co., or address 

F. I. WHITNEY, G. P. d, T. A., 

ST. PAUL, MINN. 



236 



* TAKE THE * 

Northern 
Pacific 
Railroad. 

rhe "DlnlDg Car Line 



AND 




"STellOTTT-storLe ^ ^ ^ ^ 
^ ^ ^ ^ :F>a,r:fe I3o-u.te" 



TO ALL PRINCIPAL POINTS IN 



The Greatjorthwest 

For Rates, Time-Tables and Illustrated 
Tourists' Publications, address 

J. N. HANNAFORD, CHAS. S. FEE, 

Gen'l Traffic Manager. Gen'l Pass. & Ticket Agent. 

St. :F»a,-a.l, l^^lrurL. 



Northern Pacific 
Railroad. 



23' 




[IMPROVED. I 



Igest in the \Y)orld. 

Specially adapted to high pressure 

service for running machinery of all 

kinds, from }4 to 15 horse-power. 



M 



mn 



Manufacturers of 




Little Giant Water Motors. 

The B. C. Standard Electric 

Motors and Dynamos, the Combined Water Motor 

and Dynamo, Combined Engines and Dynamos, 

Water Motor Cyclone Coffee Mills, and Electric Motor Church 
Organ Piston Motors. Also all other Electrical Supplies. 




238 



ROOT'S 

Steel or Iron Spiral Riveted Pipe 

3 to 24 inches diameter. 2 to 25 feet lengths. 

Connections and Fittings to suit service 

required. Unrivaled for 

Water Works, Huiraiflic Mining 



AND 



IRRIGATION, 

A.S HAS BEEN PROVED BY 

14 2jeaF? PFaEtical SxpepienGG. 

(See pages 24, 122, 123 herein.) 



Facfory at 

Greenpoint, L. I. 



New Yori< Office 

28 Cliff Street. 



Pacific Coast Office, 23 Davis Street, 
San Francisco, Cal. 

A. L. ALDERSON, Representing GEO. F. EBERHARD, Mgr. 



ABENDROTH & ROOT MFG. CO. 

(See next page also.) 



239 



(See page 238.) 



a, 

• 1— I 

u 

0) 

-4— > 

QJ 
> 

5-1 

cn 




Abendroth & Root 
Mfg. Co.: 

Bolt€tt Joint Section. 




240 



YOUNG &. SONS, 



Manufacturers of 



Engineering, Mining, and Sur- 
veying Instruments. 




Established 1820, 



No. 43 North Seventh 8t., Philadelphia. 



241 



DRAINAGE LEVELS. 



5Er;d foF our Special Ligt o! 

I^rainage l^eY)els 



Mailed to any address upon application 



TO 



YOUNGS SONS, 



NO. 43 NORTH 7TH ST., PHILADELPHIA, 



242 



Robinson ^ Garg Go., 



JOBBERS OF 



IrougM 
Iron 




PUMPS, 



ENGINES, 



FITTINGS, 



*C. 



VALVES. 



BOILERS. 



MACHINERY. 



Railway, Miners' & Mill Supplies 



4.TH & WACOUTA ST3., 



St. Paul, - Mmnesota. 



243 



Swan Bros., 

Well :0riller5, 

ANDOVER, SOUTH DAKOTA. 



^BY THEIR DEEDS SHALL YE KNOW THEM/' 




We have drilled wells in all parts of the Dakotas, in Wis- 
consin, Iowa, Minnesota and in the Canadian Northwest. 
We are always successful. We use the best rigs, tools, and 
machinery, and we are acknowledged to be the best drillers 
in this field. We let our work speak for us. 
Correspondence solicted. 



244 




Time Tested, Best and Cheapest Automatic Steam Vacuum Pump Known, 
for Irrigation, Mining and General Farm Purposes. 




■^ 



Has no 
Piston Rods , 
Cranks, Eccen- 
trics, Levers, 
Beams, Jets, 

Weights or 
other Compli- 
cated Mechan- 
ism to get out 
of order and 
absorb power. 



* 



Requires Less Steam and Fuel than other Pumps. 
OPERATES HUNG UP OR STATIONERY. 

ANYBODY CAN OPERATE IT 

IT WILL NEVER WEAR OUT, 

Catalogues, Estimates and Particulars Furnished on Application 

TO 

THE PULSOMETER STEAM PUMP CO., 

Sole Owner and Manufacturer, 

NEW YORK. 

See also pages 126, 127, 128 . 



245 




ARTESIAN IRRIGATION IN ITS PERFECTION. 

Where power of well is used for Threshing and Grinding Feed. 



\ . We BAiy , Irngat^e, and SeW l^and. 

Z. XHe Sink. Rr\.esiaii WeWs \)y 
Coi\\;raG\j. 

3. We Ben\. 1a and and Pay Taxes 

lor Hon-residenls and Corpo- 
ral,ions. 

4. We Sell \lie Besl Paying and 

Salesl Seonrilies in \.l\e \3 . S. • 

^ Investigate ns. 

T^be l^al^ota Irrigation Qo.^ 

ABERDEEN, S. D. 

S. W. Narregang, President, Excelsior Block. 



246 

The Western Wheeled Scraper Co., 

AURORA, ILL. 

(Formerly of Mount Pleasant, Iowa.) 

THE LEADING MANUFACTURERS OF 
GRADING IMPLEMENTS. 

Our celebrated 

Western Wheeled 
SCRAPERS 

are used in all parts of 
the world. Our 

Western Double- 
bottom Drag 
SCRAPERS 

are unequaled and are 
the favorite with all 
graders. 

We make the MOORE IRRIGATING DITCHER which is 
extensively used in all the Western States for making Irri- 
gating Ditches and laterals, and for leveling land. We also 
make the 

^est Road TVl^icbine on Gartb. 

Also Wheelbarrows, Dump-Carts and Farm Wagons. 
Send for Catalogues and Prices to the 

Western ^heeled Scraper G^.* 

AURORA, ILLS. 





247 



STEAM VACUUM PUMPS 



FOR 



IRRIGATION, Etc. 

T\ie CtieapesX;, 

T\Ae SimplesY., 

and \,\ie iiios\. 

The pump works equally well if the water is loaded with 

sand or gravel . 



Ho P\s\.ons, lio par\.s \o Wear or Break. 

Any man or boy can manage it. 
(See page 126.) 



Please write for Catalogue and full information, to the 

NYE STEAM VACUUM PUMP CO., 

7 and 9 S. Jeffers »n St., Chicago, 111. 



248 



500FOOT 
MA GfllNE 
set up in SO 
MINUTES. 




ri;V7 ONE 

can 
RUN IT, 



later Your Farms and Irrigate Your Lands 



WITH THE VERY BEST AND CHEAPEST 

53[rtesian \Y)ell TYldcbineri/. 

For wells 2,000 feet or less ten sizes set up and has the 
well half way down before an ordinary "Derrick" could be 
built. Drills 30 to 80 feet per 24 hours in hprd rock. Manu- 
factured in the great oil fields of Pennsylvania. No extras 
needed with these machines. Made with or without "trac- 
tion attachment." Our 2,000 foot rig can be run by a 
thresher engine. Buy one and make money with your idle 
thresher engine the year round. A skilled operator sent 
free to set and start each machine and give full instructions 
in its use. Every machine guaranteed. 

Correspondence solicited from parties wanting artesian wells. 

SOLD DIRECT TO USERS AT 

MANUFACTURERS PRICES. 

Catalogue of Artesian Irrigating 

:ftj:m:i=s 

for wind or steam pow- 
er. Can be run wich a 
thresher engine. Will 
save 50 per cent, of 
power, and do more 
work than any other 
pump. 

KEYSTONE 

DRILLER CO., 

Beaver Falls, Penn. 




249 

Now is the Time to Subscribe. 






Harper's Magazine, One Year - $4.00 

Harper's Weekly, One Year - - 4.0o 
Harper's Bazar, One Year - - 4.0o 
Harper's Young People, One Year, 2.0o 

i!^' Postage free to all subscribers in the 

United States, Canada, and Mexico. 

The Volumes of the Weekly and 
Bazar begin with the first numbers for 
January, the Volumes of the Young 
People with the first number for Novem- 
ber, and the Volumes of the Magazine 
with the Numbers for June and Decem- 
ber of each year. 

Booksellers and Postmasters usually 
receive subscriptions. Subscriptions sent 
direct to the publishers should be accom- 
panied by Post-Office Money Order or 
Draft. When no time is specified, sub- 
scriptions will begin with the current 
Number. 

The Magazine is an overflowing store 
of good literature and exquisite art— a 
delightful production deserving all the 
fame and the material success which have 
been won by it. The Weekly is a rarely 
illustrated chronicle of the year's events; 
there is no end of pleasure and profit in 
its pages. The Bazar is a repository of 
fashion, and a gallery of some of the finest 
engravings of the time. The Young 
People is a treasure-house fascinating to 
every boy and girl as well as to plenty of 
persons older. A remarkable and valu- 
able, an instructive and delightful line of 
publications, indeed.— iV. Y. Sun. 

A-ddress: 

HARPER & BROTHERS, 
Franklin Square, New York City. 



250 

JOHN H. MILLER. PRES. JOHN L. PYLE^ SEC. 

W. N. COLER, VICE PRES. ALVA E. TAYLOR, TREAS' 



Valley Land and Irrigation Company, 



HURON, SOUTH DAKOTA. 



Capital Stock, $2,000,000. Incorporated 1891. 



100,000 Acres of Farm Lands in 
THE ARTESIAN BELT 

For Sale on Easy Terms. 



Address: 

NORTH AMERICAN LOAN & TRUST CO., Agents, 

190 and 192, Dearborn St., Chicago, 111. 



First National Bank 

UNITED STATES DEPOSITORY. 

HURON, SOUTH DAKOTA. 

(^aipiteLl, $7^,000. garplas, $1^,000. 



H Gei^EFal Bankiijg Bu^iijE^? GFan^actEd. 



THOS. H. CAMPBELL, President. 
J. W. MACKENZIE, Cashier. 
ED. J. MILLER, Assistant Cashier. 



251 



ARTESIAN IRRIBATION 

Consolidated 
Land and * Irrigation 

Company, 

HURON. SOUTH DAKOTA. 



"Pi {Reliable Tl^edium for 
both ^u^erand 
Seller of goutb Qal^ota 



m I^ands. 



JOHN E. DIAMOND3 PRESIDENT. 

D. L. BUSH, VICE-PRESIDENT. 

M. H. PRICHARDj SEC. & TREAS. 

R. O. RICHARDS, MANAGER. 



l^and Irrigated, Soaght, Sold 
and AAanaigsd. 



251 A 



See Advertisements 

OF 

W. p. BUTLIB 



ON 



pages 2 and 41. 



251 B 

Of Making Many Books There is no End. 



(Remember W)c 7Vl<^""^^oturc 

Coilntii RBGorils, Bank Books, and 
all Kinds of Blank Books. 



Send ill your Magazines and have them 
Bound in Handsome Volumes, English Tree 
Calf, and Red Undergilt Edges down to the 
cheapest styles. Preserve your old Books and 
send them in. 



^ull C^J^€: of C^^^cil I^lanl^s. 



Send Your Orders to Us- Save Money and Time, 
Mail Orders Promptly Attended to. 



The Largest and Best Equipped 
yob Office in the State, 

Send loF Bampk GopiE3 of the Bailu and 
Weeklg F^uFoi^itE. 

SHANNON A LONBSTAFF, 

H:XJK.OI^T, S. ID. 



252 

American Well Works, 

(Or II and 13 So. Canal St., Chicago, 111,; Dallas, Texas; and! 
Sydney, N. S. W. Australia.) 

Manufacture the Largest Variety of 

WATER WELL, OIL, GAS. AND 
PROSPECTING MACHINERY, 

Operated by Horse or Steam Power; suitable for any SIZE HOLE„ 
to any depth, through any formations or com- 
bination of formations. 

Interested parties should send for Catalogue illustrating and 
describing our new 

lEliptioail l^i^illixig- IM^aoliine^ 

Combined with either the Revolving, jetting. Rope or 
Pole tools. Also describing and illustrat- 
ing all styles of 

STEAM PUMPS, BRASS VALVES, 

Deep Water Cylinders & Valves, 

PIPE, PIPE FITTINGS, &c. 

NOV 2P; b^b 







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